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Physics

Physics Study Guide Expanded Edition

9 Units · 142 Quiz Questions · 72 Flashcards · Diagnostic · Full Reference Tables · Diagrams · Saved Progress

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Position, displacement, and distance
Position locates an object relative to an origin. Displacement is the vector change in position (final − initial); distance is the total path length traveled, always ≥ |displacement|.
  • Displacement Δx = xf − xi is a vector — it has direction and can be negative or zero even if the object moved
  • Distance is scalar — always positive, equals total path length regardless of direction changes
  • If a runner goes 50 m east then 20 m west, distance = 70 m but displacement = 30 m east
  • Displacement can be zero for a round trip even though distance traveled is large
  • Position is measured relative to a chosen reference point (origin) and a chosen positive direction
Velocity vs speed
Velocity is the vector rate of change of displacement; speed is the scalar rate of change of distance.
  • Average velocity = Δx/Δt (vector, can be negative); average speed = total distance/total time (scalar, always ≥0)
  • Instantaneous velocity is the slope of the tangent line on a position-time graph at a specific instant
  • Constant velocity → straight line on position-time graph; the slope equals the velocity
  • A negative velocity means motion in the negative direction, not 'slow' motion
  • Average speed can exceed the magnitude of average velocity whenever the path is not a straight line in one direction
Acceleration
Acceleration is the vector rate of change of velocity, a = Δv/Δt. An object accelerates whenever its speed OR direction changes.
  • a = (vf − vi)/t; units are m/s²
  • Acceleration is the slope of a velocity-time graph
  • Positive acceleration does not always mean speeding up — it means speeding up if a and v have the same sign, slowing down if opposite signs
  • An object can have zero velocity but nonzero acceleration (e.g., the top of a thrown ball's path, or a car at the instant it starts moving)
  • Uniform (constant) acceleration produces a straight line on a v-t graph and a parabola on an x-t graph
The kinematic equations (constant acceleration)
These four equations relate displacement, initial/final velocity, acceleration, and time — use whichever two knowns match three variables you need.
  • vf = vi + at (no displacement term)
  • Δx = vi·t + ½at² (no final velocity term)
  • vf² = vi² + 2aΔx (no time term)
  • Δx = ½(vi + vf)t (no acceleration term)
  • Always define a positive direction first and assign signs to vi, vf, a, and Δx consistently
  • Free fall: a = −g = −9.8 m/s² (taking up as positive), same for all objects regardless of mass (ignoring air resistance)
Graphical analysis of motion
Position-time, velocity-time, and acceleration-time graphs are linked by slope and area relationships.
  • Slope of x-t graph = velocity; slope of v-t graph = acceleration
  • Area under a v-t graph = displacement; area under an a-t graph = change in velocity
  • A curved (parabolic) x-t graph indicates constant nonzero acceleration
  • A horizontal line on a v-t graph indicates constant velocity (zero acceleration)
  • An object at rest is shown as a horizontal line on an x-t graph at nonzero slope-zero (flat line)
Projectile motion
A projectile undergoes independent, simultaneous horizontal (constant velocity) and vertical (constant acceleration g) motion. The two directions never affect each other.
  • Horizontal: vx stays constant (no horizontal force if air resistance ignored); x = vx·t
  • Vertical: vy changes due to gravity; vy = vyi − gt and y = vyi·t − ½gt²
  • Time of flight for a projectile launched and landing at the same height: t = 2vyi/g
  • Maximum height occurs when vy = 0: hmax = vyi²/(2g)
  • Range is maximized at a launch angle of 45° (for equal launch/landing height, no air resistance)
  • A horizontally launched projectile (vyi = 0) falls the same vertical distance in a given time as an object simply dropped from rest
Negative acceleration is NOT the same as slowing down — it depends on the sign of velocity too.
Distance ≥ |displacement| always; they're equal only for straight-line, one-direction motion.
At the peak of projectile motion, vy = 0 but vx is unchanged and acceleration is still −g (not zero).
'Free fall' acceleration is the same for all masses — heavier objects do NOT fall faster (ignoring air resistance).
vf = vi + at
Δx = vi t + ½at²
vf² = vi² + 2aΔx
Δx = ½(vi+vf)t
Newton's First Law (inertia)
An object at rest stays at rest, and an object in motion stays in motion at constant velocity, unless acted on by a net (unbalanced) external force.
  • Inertia is the tendency of an object to resist changes in its motion; mass is the quantitative measure of inertia
  • Constant velocity (including zero) means the net force is zero — this is 'equilibrium'
  • A passenger lurches forward when a car suddenly stops because their body's inertia keeps it moving forward
  • Balanced forces (net force = 0) do NOT mean no forces are acting — they mean the forces cancel
Newton's Second Law (F = ma)
The net force on an object equals its mass times its acceleration. Acceleration is directly proportional to net force and inversely proportional to mass.
  • Fnet = ma; acceleration is always in the same direction as the net force
  • Doubling the net force doubles acceleration (mass constant); doubling the mass halves acceleration (force constant)
  • Weight is a force: Fg = mg, where g = 9.8 m/s² near Earth's surface
  • Mass is constant and measures amount of matter (kg); weight is a force that depends on local gravity (N) and changes on the Moon or in orbit
  • To solve dynamics problems: draw a free-body diagram, sum forces along each axis, set Σ F = ma per axis
Newton's Third Law (action-reaction)
For every action force one object exerts on a second object, the second exerts an equal and opposite force back on the first.
  • Action-reaction pairs act on DIFFERENT objects — they never cancel each other out on the same object
  • Forces in a pair are equal in magnitude, opposite in direction, and of the same type (both contact or both field forces)
  • A rocket accelerates forward because it pushes exhaust gas backward and the gas pushes the rocket forward
  • When you push on a wall, the wall pushes back on you with equal force — that's why you don't fall through it
Free-body diagrams & force types
A free-body diagram isolates one object and shows every external force acting on it as an arrow, with length roughly proportional to magnitude.
  • Normal force (FN): perpendicular to the contact surface, prevents objects from passing through each other
  • Weight/gravity (Fg = mg): always points straight down toward Earth's center
  • Applied force (Fa): any external push or pull
  • Tension (FT): pulling force transmitted through a string/rope/cable, directed along the rope
  • On a flat horizontal surface with no other vertical forces: FN = mg; on an incline, FN = mg·cosθ
Friction
Friction is a contact force that opposes relative sliding (or tendency to slide) between two surfaces, parallel to the surface.
  • Static friction (fs) acts before motion starts and can vary up to a maximum: fs,max = μs·FN
  • Kinetic friction (fk) acts once sliding occurs: fk = μk·FN, and is generally slightly less than max static friction
  • μ (coefficient of friction) is a unitless ratio depending on the two surfaces in contact — it does not depend on contact area
  • Friction always opposes the direction of relative motion (or attempted motion), never aids it
  • On an incline: the friction force is μ·FN = μ·mg·cosθ, while the component of gravity along the incline is mg·sinθ
Equilibrium & net force problems
When acceleration is zero, all forces balance in every direction (ΣFx = 0 and ΣFy = 0).
  • For an object at rest or moving at constant velocity, the net force is exactly zero
  • Resolve forces into x and y components using sinθ/cosθ before summing
  • Tension in a rope holding a hanging mass at rest equals the weight of the mass
  • For an object on a frictionless incline held stationary by a rope parallel to the incline, tension = mg·sinθ
A net force of zero means constant velocity (which includes rest) — NOT necessarily no motion.
Action-reaction pairs act on two different objects, so they can never produce equilibrium on a single object.
Mass and weight are not the same — mass (kg) is constant; weight (N) = mg changes with gravity.
Friction depends on the normal force and μ, NOT on the surface area of contact.
Fnet = ma
Fg = mg
ff = μFN
Diagram
mg FN mg sinθ θ

Free-body diagram of a block on a frictionless incline: weight (mg) resolves into a component along the slope (mg sinθ) and a component into the surface (mg cosθ), balanced by the normal force.

Momentum & impulse
Momentum (p = mv) describes an object's 'quantity of motion.' Impulse (J = FΔt) is the change in momentum produced by a force acting over time.
  • p = mv; a vector, same direction as velocity; units kg·m/s
  • Impulse-momentum theorem: J = FΔt = Δp = m(vf − vi)
  • Extending the time of impact (padding, airbags, bending knees on landing) reduces the force for the same impulse/momentum change
  • A larger force over a shorter time can deliver the same impulse as a smaller force over a longer time
Conservation of momentum
In a closed, isolated system (no external net force), total momentum before an interaction equals total momentum after.
  • m1v1i + m2v2i = m1v1f + m2v2f for a two-object collision or explosion
  • Momentum is conserved in ALL collisions (elastic and inelastic) as long as the system is isolated
  • Assign a positive direction and keep velocity signs consistent — objects moving in opposite directions have opposite-signed velocities
  • In an explosion (objects initially at rest flying apart), total momentum before = 0, so the pieces' momenta must be equal and opposite
Elastic vs inelastic collisions
Both types conserve momentum, but only elastic collisions also conserve total kinetic energy.
  • Elastic collision: momentum conserved AND kinetic energy conserved (objects bounce apart, no permanent deformation)
  • Inelastic collision: momentum conserved but kinetic energy is NOT conserved (some KE converts to heat, sound, deformation)
  • Perfectly (totally) inelastic collision: the objects stick together and move with a common final velocity — maximum KE loss for given momentum
  • For a perfectly inelastic collision: v_f = (m1v1i + m2v2i)/(m1+m2)
Work & the work-energy theorem
Work is done when a force causes displacement in the direction of the force. The net work done on an object equals its change in kinetic energy.
  • W = F·d·cosθ, where θ is the angle between the force and displacement vectors
  • If force is perpendicular to displacement (θ=90°), no work is done (e.g., normal force on level ground, centripetal force)
  • Work-energy theorem: Wnet = ΔKE = KEf − KEi
  • Work is a scalar; positive work adds energy to the object, negative work removes energy
  • Units: joule (J) = N·m = kg·m²/s²
Kinetic and potential energy
Kinetic energy is energy of motion; potential energy is stored energy due to position or configuration.
  • KE = ½mv² — always positive (or zero), depends on speed squared
  • Gravitational PE = mgh, relative to a chosen reference height (h=0 level is arbitrary)
  • Elastic (spring) PE = ½kx², where k is the spring constant and x is displacement from equilibrium
  • Doubling speed quadruples kinetic energy (v² dependence); doubling height doubles gravitational PE (linear)
Conservation of mechanical energy
In the absence of friction/air resistance, total mechanical energy (KE + PE) of a system stays constant — energy converts between forms but the total is unchanged.
  • KEi + PEi = KEf + PEf when only conservative forces (gravity, springs) act
  • As a pendulum or roller coaster descends, PE converts to KE; as it rises, KE converts back to PE
  • If friction or air resistance acts, total mechanical energy decreases — the 'lost' energy converts to heat/sound (total energy of the universe is still conserved)
  • At the lowest point of a swing, all the initial PE (relative to that point) has converted to KE if no friction acts: mgh = ½mv²
Momentum is conserved in EVERY collision type; kinetic energy is only conserved in elastic collisions.
A force perpendicular to displacement does ZERO work, even if the object moves (e.g., circular motion, carrying a bag horizontally).
KE depends on v² — doubling speed quadruples KE, it does not just double.
'Mechanical energy conserved' only applies when friction/air resistance/other non-conservative forces are absent or negligible.
p = mv
J = FΔt = Δp
W = Fd cosθ
KE = ½mv²
PEgrav = mgh
Uniform circular motion
An object moving in a circle at constant speed continuously changes direction, so it is always accelerating toward the center — even though its speed doesn't change.
  • Centripetal acceleration ac = v²/r, always directed toward the center of the circle
  • Velocity is always tangent to the circle, perpendicular to the centripetal acceleration
  • 'Centripetal' means center-seeking — it describes direction, not a new/separate type of force
  • Period T is the time for one full revolution; speed v = 2πr/T
  • An object moving at constant speed in a circle has changing velocity (direction changes) — so it IS accelerating despite constant speed
Centripetal force
Centripetal force is the net inward force required to keep an object moving in a circle; it is supplied by some real force (tension, gravity, friction, normal force) — it is not an independent force of its own.
  • Fc = mac = mv²/r, always directed toward the center
  • For a car turning on a flat road, friction between tires and road supplies the centripetal force
  • For a ball on a string swung horizontally, tension supplies the centripetal force
  • For a satellite orbiting a planet, gravity supplies the centripetal force
  • There is no outward 'centrifugal force' acting on the object in an inertial (non-rotating) reference frame — the outward feeling is inertia (the object 'wants' to travel in a straight line)
Newton's Law of Universal Gravitation
Every mass attracts every other mass with a force proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
  • Fg = Gm1m2/r², where G = 6.67×10⁻¹¹ N·m²/kg²
  • Doubling the distance between two masses reduces gravitational force to 1/4 (inverse square law)
  • Doubling one mass doubles the gravitational force between the two objects
  • Gravitational force is always attractive and acts along the line connecting the two masses' centers
  • r is measured center-to-center, not surface-to-surface
Orbital motion
A satellite in a stable circular orbit is in free fall around a planet — gravity provides exactly the centripetal force needed for its orbital speed and radius.
  • Setting Fg = Fc: Gm1m2/r² = m2v²/r → orbital speed v = √(Gm1/r)
  • A satellite in a larger orbit (larger r) moves at a slower orbital speed
  • Orbital speed and period do not depend on the mass of the orbiting satellite — only on the central mass and orbital radius
  • An object in orbit is continuously falling toward the planet but its tangential velocity keeps it from hitting the surface
Kepler's Laws (basics)
Kepler's three laws describe planetary orbital motion, later explained by Newton's gravitation.
  • 1st Law: planets orbit the Sun in ellipses, with the Sun at one focus
  • 2nd Law: a line from the Sun to a planet sweeps out equal areas in equal times — planets move faster when closer to the Sun (perihelion), slower when farther (aphelion)
  • 3rd Law: T² ∝ r³ — the square of the orbital period is proportional to the cube of the average orbital radius, same proportionality constant for all bodies orbiting the same central mass
There is no real outward 'centrifugal force' on the orbiting/circling object in an inertial frame — only a net inward (centripetal) force.
Centripetal force is not a new force type — it's the net result of real forces (gravity, tension, friction, normal) pointing inward.
Gravitational force follows an inverse-SQUARE law: doubling distance cuts force to 1/4, not 1/2.
Orbital speed/period depend on the central mass and orbital radius, NOT on the orbiting object's own mass.
ac = v²/r
Fc = mv²/r
Fg = Gm1m2/r²
T² ∝ r³ (Kepler's 3rd law)
Diagram
Fc (toward center) v (tangent)

Centripetal force always points toward the center of the circular path, perpendicular to the object's velocity, which is tangent to the circle.

Describing waves
A wave transfers energy through a medium (or vacuum, for EM waves) without transferring matter. Key properties describe its shape and behavior.
  • Wavelength (λ): distance between two successive identical points (crest-to-crest or compression-to-compression), in meters
  • Frequency (f): number of complete cycles per second, in hertz (Hz); f = 1/T where T is the period
  • Amplitude: maximum displacement from equilibrium; relates to the energy/intensity carried by the wave (NOT to speed or frequency)
  • Wave speed: v = fλ — determined by the medium's properties, NOT by frequency or amplitude
  • Increasing frequency while speed stays constant (same medium) causes wavelength to DECREASE proportionally
Transverse vs longitudinal waves
Waves are classified by the relationship between the direction of particle vibration and the direction of energy travel.
  • Transverse wave: particles vibrate perpendicular to the direction of wave travel (e.g., light, waves on a string) — has crests and troughs
  • Longitudinal wave: particles vibrate parallel to the direction of wave travel (e.g., sound) — has compressions (high pressure/density) and rarefactions (low pressure/density)
  • Sound cannot travel through a vacuum because it requires a medium (particles to compress/rarefy); light can travel through a vacuum
  • Sound travels fastest in solids, slower in liquids, slowest in gases, because particles are closer together and transmit vibrations more efficiently
Wave interference
When two or more waves overlap in the same medium, their displacements add algebraically (superposition).
  • Constructive interference: waves in phase add together, producing a larger amplitude (crest+crest, or compression+compression)
  • Destructive interference: waves out of phase partially or fully cancel, producing smaller (or zero) amplitude
  • After waves pass through each other, each continues on as if the interference never happened (waves don't permanently alter each other)
  • Standing waves form when two identical waves travel in opposite directions in a confined medium, creating fixed nodes (no displacement) and antinodes (maximum displacement)
The Doppler effect
The Doppler effect is the apparent shift in observed frequency (and pitch/wavelength) caused by relative motion between a wave source and an observer.
  • Source moving toward observer: sound waves bunch up in front → observer hears a HIGHER frequency (shorter wavelength)
  • Source moving away from observer: waves stretch out → observer hears a LOWER frequency (longer wavelength)
  • The actual frequency emitted by the source does not change — only the frequency perceived by the observer changes
  • Classic example: an ambulance siren sounds higher-pitched as it approaches and lower-pitched as it moves away
  • The Doppler effect applies to all waves, including light (redshift/blueshift of stars)
Sound properties
Sound is a longitudinal pressure wave; its perceived qualities relate directly to physical wave properties.
  • Pitch corresponds to frequency — higher frequency = higher pitch
  • Loudness corresponds to amplitude/intensity — larger amplitude = louder sound
  • Speed of sound in air at room temperature ≈ 343 m/s (increases with temperature)
  • Resonance occurs when a system is driven at its natural frequency, producing a dramatic increase in amplitude
Wave speed depends on the medium, not on frequency or amplitude — changing frequency changes wavelength, not speed (same medium).
Amplitude relates to energy/loudness, NOT to wave speed or frequency.
Sound needs a medium and cannot travel through a vacuum; light/EM waves can.
In the Doppler effect the SOURCE's emitted frequency never changes — only what the observer perceives changes.
v = fλ
f = 1/T
Electric charge & Coulomb's Law
Charge is a fundamental property of matter; like charges repel, opposite charges attract, following an inverse-square law similar in form to gravity.
  • Charge is quantized: q = ne, where e = 1.6×10⁻¹⁹ C (elementary charge) and n is an integer
  • Charge is conserved: total charge in an isolated system stays constant (charge is transferred, not created/destroyed)
  • Coulomb's Law: Fe = kq1q2/r², where k = 8.99×10⁹ N·m²/C²
  • Doubling the distance between two charges reduces the electric force to 1/4 (inverse-square, like gravity)
  • Unlike gravity (always attractive), the electric force can be attractive (opposite charges) or repulsive (like charges)
Electric fields
An electric field is the region around a charge where another charge would feel a force; field lines show the direction a positive test charge would move.
  • E = F/q (force per unit positive test charge), units N/C
  • Field lines point AWAY from positive charges and TOWARD negative charges
  • Field lines never cross; closer spacing indicates a stronger field
  • Inside a uniform field (e.g., between parallel plates), the field is constant in magnitude and direction
  • A charge placed in an external field experiences a force F = qE in the direction of E (for positive q) or opposite E (for negative q)
Ohm's Law & circuit basics
Ohm's Law relates voltage, current, and resistance in a circuit element.
  • V = IR, where V is potential difference (volts), I is current (amperes), R is resistance (ohms, Ω)
  • Current is the rate of charge flow: I = q/t, conventionally defined as the direction positive charge would flow
  • Resistance depends on a material's resistivity, length (directly), and cross-sectional area (inversely): R = ρL/A
  • Power dissipated: P = IV = I²R = V²/R
Series circuits
In a series circuit, there is only one path for current, so every component shares the same current.
  • Current is the SAME through every component: Itotal = I1 = I2 = I3
  • Total resistance is the SUM of individual resistances: Rtotal = R1 + R2 + R3
  • Voltage divides across components in proportion to their resistance: Vtotal = V1 + V2 + V3
  • If one component fails (opens), the entire circuit stops — no current flows anywhere
Parallel circuits
In a parallel circuit, components are connected across common nodes, giving multiple paths for current.
  • Voltage is the SAME across every parallel branch: Vtotal = V1 = V2 = V3
  • Current divides among branches, with more current through lower-resistance branches: Itotal = I1 + I2 + I3
  • Total resistance is found from 1/Rtotal = 1/R1 + 1/R2 + 1/R3, and is always LESS than the smallest individual resistor
  • If one branch fails (opens), current still flows through the other branches — the rest of the circuit keeps working
In series circuits current is the same everywhere; in parallel circuits voltage is the same across each branch — don't mix these up.
Total parallel resistance is always SMALLER than the smallest individual resistor, not larger.
Electric force can attract OR repel; gravity is only ever attractive.
Field lines point away from positive charges and toward negative — not the reverse.
Fe = kq1q2/r²
E = F/q
V = IR
P = IV = I²R = V²/R
Rseries = R1+R2+... ; 1/Rparallel = 1/R1+1/R2+...
Diagram
Series Parallel

Series circuit (same current everywhere, resistances add) vs parallel circuit (same voltage across each branch, resistances combine reciprocally).

Magnetic fields
Magnetic fields are produced by moving charges (currents) and by certain materials (permanent magnets); field lines run from north to south pole outside the magnet.
  • Every magnet has two poles (north and south) — magnetic monopoles have never been observed
  • Like poles repel; opposite poles attract
  • Outside a magnet, field lines point from the north pole to the south pole; inside the magnet they continue from south back to north, forming closed loops
  • A moving electric charge creates its own magnetic field circling around its direction of motion
  • A current-carrying wire produces a magnetic field that circles the wire — direction given by the right-hand rule (thumb along conventional current, fingers curl in the field direction)
Force on a moving charge / current-carrying wire
A magnetic field exerts a force on a moving charge (or current), but only on the component of velocity perpendicular to the field.
  • F = qvB sinθ, where θ is the angle between velocity and the magnetic field; force is zero if v is parallel to B
  • Direction of force on a positive charge: right-hand rule — fingers point along v, curl toward B, thumb gives F (or F = qv×B)
  • The magnetic force on a moving charge is always perpendicular to both v and B, so it changes direction, not speed — it does no work on the charge
  • A current-carrying wire in a magnetic field experiences F = BIL sinθ (L = length of wire in the field)
  • Charged particles moving perpendicular to a uniform B field move in a circular path (the magnetic force supplies the centripetal force)
Electromagnetic induction
A changing magnetic flux through a loop of wire induces an EMF (voltage) in that loop — the basis of generators and transformers.
  • Faraday's Law: induced EMF is proportional to the rate of change of magnetic flux through a circuit
  • Flux can change by varying the field strength, the area of the loop, or the angle between the loop and the field
  • Lenz's Law: the induced current flows in a direction that opposes the change in flux that created it (conservation of energy)
  • No induction occurs if the magnetic flux through the loop is constant — motion (or change) is required, not just presence of a field
  • Moving a magnet faster through a coil, or using more coil turns, increases the induced EMF
Generators and motors
Generators and motors are essentially the same device used in opposite ways — one converts mechanical energy to electrical, the other electrical to mechanical.
  • A generator rotates a coil within a magnetic field (or a magnet within a coil), inducing an alternating EMF via electromagnetic induction
  • A motor passes current through a coil in a magnetic field; the resulting force on the current-carrying wires produces torque that spins the coil
  • Both rely on the same underlying interaction between current, magnetic fields, and motion — just with cause and effect reversed
  • AC generators produce alternating current because the coil's orientation relative to the field continuously changes as it rotates
The magnetic force on a moving charge is zero if velocity is parallel to B, not just small — check the sinθ factor.
Magnetic force is always perpendicular to velocity, so it changes direction but never speeds up or slows down a charge (does no work).
Induction requires a CHANGING flux — a stationary loop in a constant, unchanging field induces nothing.
Magnetic monopoles don't exist — you can never isolate just a north or just a south pole.
F = qvB sinθ
F = BIL sinθ
Reflection
Reflection occurs when a wave bounces off a boundary between two media instead of passing through.
  • Law of reflection: angle of incidence = angle of reflection, both measured from the normal (a line perpendicular to the surface)
  • Specular (regular) reflection: parallel rays reflect off a smooth surface in a single direction, forming a clear image
  • Diffuse reflection: parallel rays reflect off a rough surface in many directions, no clear image forms
  • A plane mirror forms a virtual, upright, same-size image located as far behind the mirror as the object is in front
Refraction & Snell's Law
Refraction is the bending of a wave as it passes from one medium into another with a different speed (and index of refraction).
  • Index of refraction n = c/v, where c is the speed of light in vacuum and v is the speed in the medium; n ≥ 1 always
  • Snell's Law: n1 sinθ1 = n2 sinθ2, where angles are measured from the normal
  • Light bends TOWARD the normal when entering a denser (higher n, slower v) medium, and AWAY from the normal when entering a less dense medium
  • Total internal reflection occurs when light travels from a denser to a less dense medium at an angle greater than the critical angle — all light reflects, none refracts out
  • Critical angle: sinθc = n2/n1 (light going from higher n1 to lower n2)
Lenses
Lenses use refraction at curved surfaces to converge or diverge light and form images.
  • Convex (converging) lens: thicker in the middle; parallel rays converge to a real focal point on the far side
  • Concave (diverging) lens: thinner in the middle; parallel rays spread apart, appearing to diverge from a virtual focal point on the near side
  • Thin lens equation: 1/f = 1/do + 1/di, where do = object distance, di = image distance, f = focal length
  • Magnification: m = −di/do = hi/ho; negative m means an inverted image, positive m means an upright image
  • A convex lens forms a real, inverted image when the object is beyond the focal point (do > f); if do < f, it forms a virtual, upright, magnified image
Mirrors
Curved mirrors (concave and convex) form images by reflection according to the same mirror equation used for lenses.
  • Concave (converging) mirror: reflective surface curves inward; can form real, inverted images (object beyond focal point) or virtual, upright, magnified images (object inside focal point, like a shaving mirror)
  • Convex (diverging) mirror: reflective surface curves outward; always forms a virtual, upright, reduced image with a wider field of view (e.g., car side mirrors, store security mirrors)
  • Mirror equation: 1/f = 1/do + 1/di (same form as the thin lens equation)
  • Sign convention: real images and distances on the reflective side are positive; virtual images (behind the mirror) are negative
Image formation summary
Whether an image is real/virtual, upright/inverted, and magnified/reduced depends on the type of lens or mirror and the object's distance relative to the focal length.
  • Real images can be projected onto a screen; they form where light rays actually converge
  • Virtual images cannot be projected onto a screen; they form where light rays only appear to diverge from, as traced backward
  • Real images from a single converging lens/mirror are always inverted; virtual images from these are always upright
  • Diverging lenses and diverging (convex) mirrors always produce virtual, upright, reduced images, regardless of object distance
Light bends TOWARD the normal entering a denser medium, AWAY from the normal entering a less dense medium — easy to reverse.
Total internal reflection only happens going from higher n to lower n, and only past the critical angle.
A convex mirror ALWAYS produces a virtual, upright, reduced image — it never forms a real image.
Don't confuse converging (convex lens/concave mirror) with diverging (concave lens/convex mirror) — the mirror/lens naming is opposite for curvature direction.
n = c/v
n1 sinθ1 = n2 sinθ2
1/f = 1/do + 1/di
m = −di/do = hi/ho
Diagram
object image F

A converging (convex) lens: an object beyond the focal point (F) forms a real, inverted image on the far side where refracted rays converge.

The photoelectric effect
When light of sufficiently high frequency strikes a metal surface, it ejects electrons — evidence that light behaves as discrete packets of energy (photons), not just a continuous wave.
  • Photon energy: E = hf, where h = 6.63×10⁻³⁴ J·s (Planck's constant)
  • Each metal has a threshold (minimum) frequency below which NO electrons are ejected, regardless of light intensity
  • Above the threshold frequency, increasing light INTENSITY increases the NUMBER of ejected electrons (current), not their kinetic energy
  • Increasing light FREQUENCY (above threshold) increases the maximum KINETIC ENERGY of ejected electrons, not the number
  • Einstein's photoelectric equation: KEmax = hf − W0, where W0 is the work function (minimum energy needed to eject an electron)
  • This effect could not be explained by classical wave theory, which predicted intensity alone should eject electrons at any frequency
Wave-particle duality
Light and matter both exhibit properties of waves AND particles, depending on the experiment used to observe them.
  • Light behaves as a wave in diffraction/interference experiments (e.g., double-slit) but as particles (photons) in the photoelectric effect and Compton scattering
  • De Broglie proposed that all matter has an associated wavelength: λ = h/p = h/(mv)
  • Macroscopic objects have negligibly small de Broglie wavelengths (undetectable); subatomic particles (electrons) have measurable wavelengths, confirmed by electron diffraction
  • Wave-particle duality means neither a purely classical wave model nor a purely classical particle model fully describes light or matter
Atomic models & spectra
The Bohr model explained why atoms emit/absorb light only at specific, discrete wavelengths, using quantized electron energy levels.
  • Electrons exist only in specific, quantized energy levels (orbits) around the nucleus — not at arbitrary energies
  • An electron absorbs a photon of exactly the right energy to jump to a higher energy level (excitation); it emits a photon of exactly that energy when it falls back down
  • Emission spectra show bright lines at specific wavelengths corresponding to allowed electron transitions — a unique 'fingerprint' for each element
  • Photon energy emitted/absorbed equals the energy difference between two levels: Ephoton = Ehigh − Elow = hf
  • The Bohr model was later refined by the quantum mechanical model, where electrons exist in probability clouds rather than fixed circular orbits
Nuclear physics & radioactivity
Unstable nuclei spontaneously emit particles or energy (radioactive decay) to become more stable, transforming into different nuclides.
  • Alpha decay: nucleus emits a helium nucleus (2 protons + 2 neutrons); mass number decreases by 4, atomic number decreases by 2 — least penetrating, stopped by paper/skin
  • Beta decay: a neutron converts to a proton (emitting an electron/beta particle), or vice versa; mass number unchanged, atomic number changes by ±1 — moderate penetration, stopped by aluminum
  • Gamma decay: nucleus emits high-energy EM radiation (a photon) with no change in mass number or atomic number — most penetrating, needs lead/thick concrete to stop
  • Half-life: the time for half of a radioactive sample to decay; decay is a random, exponential (not linear) process independent of external conditions (temperature, pressure)
  • Nuclear fission splits a heavy nucleus into smaller nuclei (releasing energy); nuclear fusion combines light nuclei into a heavier one (releasing even more energy per unit mass, powers the Sun)
  • Mass-energy equivalence: E = mc² — a small amount of mass converts into a very large amount of energy in nuclear reactions
Increasing light intensity increases the NUMBER of photoelectrons, not their energy; increasing frequency increases their energy, not necessarily the number.
Below the threshold frequency, no electrons are ejected no matter how intense the light is.
Alpha particles are the LEAST penetrating (stopped by paper) but MOST ionizing; gamma is the MOST penetrating but least ionizing.
Half-life describes a constant PROPORTION (½) decaying per interval, not a constant number of atoms — decay is exponential, not linear.
E = hf
KEmax = hf − W0
λ = h/p
E = mc²
Practice Question Bank — 142 questions
Unit 1: Kinematics (17)
  1. A runner moves 50 m east then 20 m west. What is the runner's displacement?

    • 70 m east
    • 30 m east
    • 30 m west
    • 70 m west

    Displacement = 50 east − 20 east(since west is −) = 50 − 20 = 30 m east. Distance would be 70 m, but displacement is 30 m east.

  2. What is the total distance traveled by the runner in the previous scenario?

    • 30 m
    • 50 m
    • 20 m
    • 70 m

    Distance is the total path length: 50 m + 20 m = 70 m, regardless of direction.

  3. Which quantity is a vector?

    • Distance
    • Speed
    • Displacement
    • Time

    Displacement has both magnitude and direction, making it a vector. Distance, speed, and time are scalars.

  4. On a position-time graph, the slope represents:

    • Acceleration
    • Velocity
    • Distance
    • Displacement

    Slope of an x-t graph = Δx/Δt = velocity.

  5. On a velocity-time graph, the area under the curve represents:

    • Acceleration
    • Velocity
    • Displacement
    • Force

    Area under a v-t graph = displacement (since Δx = v·t for each small interval).

  6. An object has a positive velocity and a negative acceleration. The object is:

    • Speeding up
    • Slowing down
    • Moving at constant speed
    • Not moving

    When velocity and acceleration have opposite signs, the object is slowing down (decelerating).

  7. A car accelerates from rest at 4 m/s² for 5 seconds. What is its final velocity?

    • 9 m/s
    • 20 m/s
    • 0.8 m/s
    • 25 m/s

    vf = vi + at = 0 + (4)(5) = 20 m/s.

  8. A ball is thrown straight up. At the very top of its path, its acceleration is:

    • Zero
    • Equal to g, directed downward
    • Equal to g, directed upward
    • Undefined

    Gravity acts continuously; acceleration is always −g (downward) even at the peak where velocity is momentarily zero.

  9. An object starts from rest and accelerates uniformly at 3 m/s² for 4 seconds. How far does it travel?

    • 12 m
    • 24 m
    • 6 m
    • 48 m

    Δx = vi·t + ½at² = 0 + ½(3)(4²) = ½(3)(16) = 24 m.

  10. A projectile is launched horizontally from a cliff. Compared to an object simply dropped from the same height at the same time, the projectile:

    • Hits the ground first
    • Hits the ground later
    • Hits the ground at the same time
    • Never hits the ground

    Horizontal and vertical motions are independent; both objects have the same initial vertical velocity (0) and the same vertical acceleration (g), so they fall for the same amount of time.

  11. A ball is launched at 20 m/s at an angle of 30° above the horizontal. What is its initial vertical velocity component?

    • 20 m/s
    • 17.3 m/s
    • 10 m/s
    • 0 m/s

    vyi = v sinθ = 20 sin30° = 20(0.5) = 10 m/s.

  12. For maximum range on level ground (no air resistance), a projectile should be launched at an angle of:

    • 30°
    • 45°
    • 60°
    • 90°

    Range is maximized at 45° for equal launch and landing heights, ignoring air resistance.

  13. Which of the following can be true for an object with zero velocity?

    • It must have zero acceleration
    • It cannot have nonzero acceleration
    • It can have nonzero acceleration
    • It must be at its starting position

    An object can be momentarily at rest while still accelerating, such as a ball at the top of its toss, or a car just starting to move.

  14. A car's velocity-time graph is a horizontal line above the time axis. This means the car has:

    • Constant positive acceleration
    • Zero velocity
    • Constant nonzero velocity
    • Increasing velocity

    A horizontal (flat) line on a v-t graph means velocity isn't changing — constant velocity, zero acceleration.

  15. An object's average speed over a trip is 20 m/s. Its average velocity for the same trip:

    • Must also be 20 m/s
    • Could be less than 20 m/s in magnitude
    • Must be greater than 20 m/s
    • Must be negative

    Average speed = total distance/time; average velocity = displacement/time. Since distance ≥ |displacement|, average speed ≥ |average velocity|.

  16. A ball is dropped from rest and falls for 2.0 s. How far does it fall (use g=9.8 m/s²)?

    • 9.8 m
    • 19.6 m
    • 4.9 m
    • 39.2 m

    Δx = ½gt² = ½(9.8)(2.0²) = ½(9.8)(4) = 19.6 m.

  17. Which kinematic equation should be used if you know vi, a, and Δx, and want to find vf without knowing t?

    • vf = vi + at
    • Δx = vi t + ½at²
    • vf² = vi² + 2aΔx
    • Δx = ½(vi+vf)t

    vf² = vi² + 2aΔx is the only kinematic equation that omits time.

Unit 2: Newton's Laws & Dynamics (17)
  1. An object moves at constant velocity. What can you conclude about the net force acting on it?

    • It must be zero
    • It must equal the object's weight
    • It must be increasing
    • It cannot be determined

    Constant velocity means zero acceleration, so by Newton's Second Law, the net force must be zero.

  2. A 10 kg object experiences a net force of 25 N. What is its acceleration?

    • 250 m/s²
    • 2.5 m/s²
    • 0.4 m/s²
    • 15 m/s²

    a = Fnet/m = 25/10 = 2.5 m/s².

  3. Which pair of forces is an example of a Newton's Third Law force pair?

    • Weight and normal force on the same object
    • The force of a hammer on a nail, and the nail on the hammer
    • Tension in a rope and gravity on a hanging object
    • Friction and applied force on the same object

    Action-reaction pairs act on two DIFFERENT objects — the hammer pushes the nail, the nail pushes back on the hammer with equal and opposite force.

  4. A book rests on a table. The normal force on the book is equal in magnitude to the book's weight. This is an example of:

    • A Newton's Third Law pair
    • Two forces on the same object that happen to balance (equilibrium)
    • Centripetal force
    • Impulse

    Weight and normal force act on the SAME object (the book) and happen to balance since the book isn't accelerating vertically — NOT a third-law pair, which would require different objects.

  5. What is the weight of a 5 kg mass on Earth (g = 9.8 m/s²)?

    • 5 N
    • 49 N
    • 0.51 N
    • 5 kg

    Fg = mg = (5)(9.8) = 49 N.

  6. A box on a horizontal surface has a mass of 8 kg and a coefficient of kinetic friction of 0.3. What is the kinetic friction force (g=9.8 m/s²)?

    • 2.4 N
    • 23.5 N
    • 78.4 N
    • 0.24 N

    FN = mg = (8)(9.8) = 78.4 N. fk = μkFN = (0.3)(78.4) = 23.5 N.

  7. Which statement about mass and weight is correct?

    • Mass and weight are the same thing measured in different units
    • Mass is constant everywhere; weight depends on local gravity
    • Weight is constant everywhere; mass depends on local gravity
    • Both mass and weight change with location

    Mass (kg) measures the amount of matter and doesn't change; weight (N) = mg depends on the local gravitational field.

  8. A rope holds a 12 kg mass stationary, hanging vertically. What is the tension in the rope (g=9.8 m/s²)?

    • 12 N
    • 1.2 N
    • 117.6 N
    • 0 N

    Since the mass is in equilibrium, tension equals weight: T = mg = (12)(9.8) = 117.6 N.

  9. An astronaut has a mass of 70 kg on Earth. On the Moon, where gravity is about 1/6 of Earth's, the astronaut's mass is:

    • 70 kg still
    • About 11.7 kg
    • 420 kg
    • Zero, since there's no gravity in space

    Mass does not change with location — only weight changes. The astronaut's mass remains 70 kg on the Moon.

  10. Which of the following increases the maximum static friction force between two surfaces?

    • Increasing the contact area
    • Increasing the normal force
    • Decreasing the normal force
    • Increasing the object's velocity

    Maximum static friction fs,max = μsFN depends on the normal force (and μ), not on contact area or velocity.

  11. A block sits on a frictionless incline at angle θ. The component of gravity acting parallel to the incline surface (down the slope) is:

    • mg
    • mg cosθ
    • mg sinθ
    • mg tanθ

    The component of weight parallel to the incline is mg sinθ; the component perpendicular (balanced by normal force) is mg cosθ.

  12. Two blocks are connected by a rope over a frictionless pulley. Which law explains why the same magnitude of acceleration applies to both blocks?

    • Newton's Third Law
    • Conservation of momentum
    • The rope is inextensible, constraining both blocks to move together
    • Newton's First Law

    Because the rope doesn't stretch, both blocks must have the same speed and acceleration magnitude at all times — a constraint, not directly a Newton's law statement.

  13. Which of these is NOT one of Newton's Laws of Motion?

    • An object in motion stays in motion unless acted on by a net force
    • Force equals mass times acceleration
    • For every action there is an equal and opposite reaction
    • Energy cannot be created or destroyed

    'Energy cannot be created or destroyed' is the law of conservation of energy, not one of Newton's three laws of motion.

  14. A 1000 kg car accelerates at 2 m/s². What net force is required?

    • 500 N
    • 2000 N
    • 1000 N
    • 4000 N

    Fnet = ma = (1000)(2) = 2000 N.

  15. When you push against a wall, the wall pushes back on you with equal force. This is best explained by:

    • Newton's First Law
    • Newton's Second Law
    • Newton's Third Law
    • Conservation of energy

    Newton's Third Law: for every action force, there's an equal and opposite reaction force.

  16. An object is in equilibrium on an incline, held by a rope parallel to the incline. The tension in the rope is:

    • mg
    • mg cosθ
    • mg sinθ
    • zero

    For equilibrium along the incline, tension must balance the component of gravity along the incline: T = mg sinθ.

  17. Which best describes inertia?

    • The force that keeps objects moving
    • A property that measures the amount of gravitational force on an object
    • The tendency of an object to resist a change in its state of motion
    • The rate of change of momentum

    Inertia is the tendency of matter to resist changes in velocity (both magnitude and direction); mass is the quantitative measure of inertia.

Unit 3: Momentum & Energy (15)
  1. A 2 kg object moves at 5 m/s. What is its momentum?

    • 2.5 kg·m/s
    • 10 kg·m/s
    • 7 kg·m/s
    • 0.4 kg·m/s

    p = mv = (2)(5) = 10 kg·m/s.

  2. A 3 kg object experiences a net force of 6 N for 2 seconds. What is the impulse delivered?

    • 12 N·s
    • 3 N·s
    • 18 N·s
    • 1 N·s

    J = FΔt = (6)(2) = 12 N·s.

  3. Airbags reduce injury in car crashes primarily by:

    • Reducing the change in momentum during the crash
    • Increasing the time over which momentum changes, reducing the force
    • Increasing the force on the passenger
    • Eliminating momentum entirely

    For a fixed impulse (Δp), extending the time of impact reduces the average force (J=FΔt), which is how airbags reduce injury.

  4. Two objects of equal mass moving in opposite directions with equal speed collide and stick together. What is their final velocity?

    • Equal to the original speed
    • Zero
    • Double the original speed
    • Cannot be determined

    Total initial momentum = mv + m(−v) = 0, so by conservation of momentum, final momentum must also be zero, meaning they stop.

  5. Which type of collision conserves both momentum AND kinetic energy?

    • Perfectly inelastic collision
    • Elastic collision
    • Any collision involving a large object
    • Explosions only

    Elastic collisions conserve both momentum and total kinetic energy; inelastic collisions conserve only momentum.

  6. A 4 kg cart moving at 3 m/s collides and sticks with a stationary 2 kg cart. What is their common final velocity?

    • 1 m/s
    • 2 m/s
    • 3 m/s
    • 6 m/s

    Conservation of momentum: (4)(3) + (2)(0) = (4+2)v → 12 = 6v → v = 2 m/s.

  7. How much work is done by a 10 N force pushing an object 5 m in the direction of the force?

    • 2 J
    • 15 J
    • 50 J
    • 0.5 J

    W = Fd cosθ = (10)(5)(cos0°) = 50 J.

  8. A person carries a heavy bag horizontally at constant velocity across a room. How much work does the person do on the bag (ignoring the initial lift)?

    • A large positive amount
    • A large negative amount
    • Zero
    • Depends on the bag's weight only

    The applied force (upward, to support the bag) is perpendicular to the horizontal displacement, so W = Fd cos90° = 0.

  9. What is the kinetic energy of a 2 kg object moving at 6 m/s?

    • 12 J
    • 24 J
    • 36 J
    • 72 J

    KE = ½mv² = ½(2)(6²) = ½(2)(36) = 36 J.

  10. If the speed of an object doubles, its kinetic energy:

    • Doubles
    • Triples
    • Quadruples
    • Stays the same

    KE ∝ v², so doubling speed quadruples kinetic energy.

  11. A 5 kg object is raised 3 m above the ground. What is its gravitational potential energy relative to the ground (g=9.8 m/s²)?

    • 15 J
    • 147 J
    • 1.67 J
    • 24.5 J

    PE = mgh = (5)(9.8)(3) = 147 J.

  12. A roller coaster car at the top of a hill has PE = 5000 J and KE = 0 (ignoring friction). What is its KE at the bottom of the hill if PE there is 0?

    • 0 J
    • 2500 J
    • 5000 J
    • 10000 J

    By conservation of mechanical energy, total energy stays constant: KEf = PEi − PEf + KEi = 5000 − 0 + 0 = 5000 J.

  13. In a real roller coaster with friction, the total mechanical energy at the bottom of a hill compared to the top is:

    • The same
    • Greater, due to added KE
    • Less, because some energy converts to heat/sound
    • Undefined

    Friction is a non-conservative force that removes mechanical energy from the system, converting it to heat and sound — total energy (including heat) is still conserved, but mechanical energy decreases.

  14. Which quantity is conserved in ALL collisions, whether elastic or inelastic (assuming an isolated system)?

    • Kinetic energy
    • Momentum
    • Both momentum and kinetic energy
    • Neither

    Momentum is always conserved in an isolated system's collisions; kinetic energy is only conserved in elastic collisions.

  15. A spring with spring constant k=200 N/m is compressed 0.1 m. What is the elastic potential energy stored?

    • 20 J
    • 2 J
    • 1 J
    • 200 J

    PEspring = ½kx² = ½(200)(0.1²) = ½(200)(0.01) = 1 J.

Unit 4: Circular Motion & Gravitation (16)
  1. A car travels in a circle at constant speed. Which statement is true?

    • The car has zero acceleration since speed is constant
    • The car has acceleration directed toward the center of the circle
    • The car has acceleration directed away from the center
    • The car's velocity is constant

    Even at constant speed, direction is continuously changing, producing centripetal acceleration directed toward the center.

  2. A 1200 kg car rounds a curve of radius 50 m at 10 m/s. What centripetal force is required?

    • 240 N
    • 2400 N
    • 120 N
    • 24000 N

    Fc = mv²/r = (1200)(10²)/50 = (1200)(100)/50 = 2400 N.

  3. What force provides the centripetal force for a satellite orbiting Earth?

    • Tension
    • Friction
    • Gravity
    • Normal force

    Gravity between the satellite and Earth supplies the necessary centripetal force for circular orbit.

  4. If the distance between two masses is tripled, the gravitational force between them:

    • Triples
    • Is 1/3 as strong
    • Is 1/9 as strong
    • Is 9 times as strong

    Gravity follows an inverse-square law: Fg ∝ 1/r². Tripling r reduces force to 1/3² = 1/9.

  5. Two masses are doubled (both m1 and m2 double) while distance stays the same. The gravitational force between them becomes:

    • 2 times as strong
    • 4 times as strong
    • Half as strong
    • Unchanged

    Fg ∝ m1m2, so doubling both masses multiplies the force by 2×2=4.

  6. A ball on a string is swung in a horizontal circle. What provides the centripetal force?

    • Gravity
    • Air resistance
    • Tension in the string
    • The ball's inertia

    Tension in the string pulls the ball toward the center, providing the centripetal force.

  7. According to Kepler's Third Law, if planet A orbits at twice the radius of planet B (same central star), planet A's orbital period compared to planet B's is:

    • 2 times as long
    • 4 times as long
    • 2√2 times as long
    • Half as long

    T² ∝ r³, so TA²/TB² = (2)³ = 8 → TA/TB = √8 = 2√2 ≈ 2.83.

  8. An object moves in a circle at constant speed. Which of the following is constant?

    • Velocity
    • Centripetal acceleration direction only relative to a fixed axis
    • Speed
    • Position

    Speed (magnitude of velocity) stays constant in uniform circular motion, but velocity direction and acceleration direction continuously change (though acceleration magnitude is constant, its direction always points to the center, which itself is a changing direction in space).

  9. Universal gravitation constant G has units of:

    • N/kg
    • N·m²/kg²
    • m/s²
    • kg·m/s

    From Fg = Gm1m2/r², G must have units of N·m²/kg² so the equation balances dimensionally.

  10. A satellite orbits at a larger radius than another satellite around the same planet. Compared to the closer satellite, the farther one has:

    • A greater orbital speed
    • A smaller orbital speed
    • The same orbital speed
    • An orbital speed independent of radius

    Orbital speed v=√(Gm/r) decreases as r increases — farther satellites move slower.

  11. Why is there no real outward force acting on a passenger in a car turning a corner (in an inertial frame)?

    • Because friction cancels all forces
    • Because the passenger's inertia makes them tend to continue in a straight line, while the car curves under them
    • Because gravity pulls them outward
    • There actually IS a real outward force, called centrifugal force

    In an inertial reference frame, only a real inward (centripetal) net force acts; the sensation of being 'thrown outward' is simply the passenger's inertia resisting the change in direction.

  12. A 500 kg satellite and a 1000 kg satellite orbit Earth at the same radius. Which has the greater orbital speed?

    • The 500 kg satellite
    • The 1000 kg satellite
    • Both have the same orbital speed
    • Cannot be determined

    Orbital speed v=√(GMEarth/r) does not depend on the orbiting satellite's own mass — both have the same speed at the same radius.

  13. Kepler's Second Law states that a planet sweeps out equal areas in equal times. This implies the planet moves:

    • Fastest when farthest from the Sun
    • Fastest when closest to the Sun
    • At constant speed throughout its orbit
    • Only in a perfect circle

    To sweep equal areas in equal times while closer to the Sun (a shorter radius arm), the planet must move faster near perihelion.

  14. What is the centripetal acceleration of an object moving at 4 m/s in a circle of radius 2 m?

    • 2 m/s²
    • 8 m/s²
    • 16 m/s²
    • 4 m/s²

    ac = v²/r = (4²)/2 = 16/2 = 8 m/s².

  15. A planet's orbit is best described by Kepler's First Law as:

    • A perfect circle centered on the Sun
    • An ellipse with the Sun at one focus
    • A parabola
    • A straight line

    Kepler's First Law: planetary orbits are ellipses with the Sun at one of the two foci.

  16. If Earth's radius suddenly doubled with mass unchanged, the gravitational force on an object at the new surface would be:

    • The same
    • Twice as strong
    • Half as strong
    • One-fourth as strong

    Fg ∝ 1/r²; doubling the radius (distance to center) reduces surface gravity to 1/4.

Unit 5: Waves & Sound (15)
  1. A wave has a frequency of 5 Hz and a wavelength of 2 m. What is its speed?

    • 2.5 m/s
    • 10 m/s
    • 7 m/s
    • 0.4 m/s

    v = fλ = (5)(2) = 10 m/s.

  2. If the frequency of a wave increases while it stays in the same medium, its wavelength:

    • Increases
    • Decreases
    • Stays the same
    • Cannot be determined

    Since v=fλ and speed is fixed by the medium, increasing f must decrease λ proportionally.

  3. Sound is best classified as a:

    • Transverse wave
    • Longitudinal wave
    • Electromagnetic wave
    • Standing wave only

    Sound is a longitudinal wave — particles vibrate parallel to the direction of wave travel, creating compressions and rarefactions.

  4. Sound cannot travel through a vacuum because:

    • Sound waves are too weak in a vacuum
    • Sound requires a medium (particles) to compress and rarefy
    • The vacuum absorbs all sound energy
    • Light waves interfere with sound in a vacuum

    Sound is a mechanical wave requiring particles to transmit compressions and rarefactions; a vacuum has no particles.

  5. Sound travels fastest through which medium?

    • Air
    • Water
    • Steel (a solid)
    • Vacuum

    Sound travels fastest in solids because particles are closest together and transmit vibrations most efficiently, slower in liquids, slowest in gases.

  6. Two identical waves arrive perfectly in phase at the same point. This is an example of:

    • Destructive interference
    • Constructive interference
    • The Doppler effect
    • Refraction

    In-phase waves add their displacements together, producing a larger amplitude — constructive interference.

  7. An ambulance siren sounds higher-pitched as it approaches you and lower-pitched as it drives away. This is:

    • Resonance
    • The Doppler effect
    • Constructive interference
    • Refraction

    The Doppler effect: the source moving toward you compresses wavefronts (higher perceived frequency); moving away stretches them (lower perceived frequency).

  8. What actually happens to the siren's emitted frequency as the ambulance moves toward and then away from a stationary observer?

    • It increases then decreases
    • It decreases then increases
    • It stays exactly the same the whole time — only the perceived frequency changes
    • It becomes zero momentarily

    The source's actual emitted frequency never changes; only the frequency perceived by the observer shifts due to relative motion.

  9. Which best describes amplitude?

    • The number of cycles per second
    • The distance between two crests
    • The maximum displacement from equilibrium, related to a wave's energy
    • The speed of the wave

    Amplitude is the maximum displacement from equilibrium and relates to the energy/intensity (loudness for sound) carried by the wave.

  10. A standing wave is formed by:

    • A single wave traveling in one direction
    • Two identical waves traveling in opposite directions in a confined medium
    • Refraction at a boundary
    • The Doppler effect

    Standing waves result from the superposition of two identical waves traveling in opposite directions, creating fixed nodes and antinodes.

  11. A wave's period is 0.25 s. What is its frequency?

    • 0.25 Hz
    • 4 Hz
    • 2.5 Hz
    • 40 Hz

    f = 1/T = 1/0.25 = 4 Hz.

  12. Which property of a sound wave corresponds to its perceived pitch?

    • Amplitude
    • Wavelength only, independent of frequency
    • Frequency
    • Speed

    Pitch corresponds directly to frequency — higher frequency sounds are perceived as higher pitch.

  13. Points of maximum displacement in a standing wave are called:

    • Nodes
    • Antinodes
    • Crests only
    • Rarefactions only

    Antinodes are points of maximum displacement; nodes are points of zero displacement.

  14. Resonance occurs when:

    • A wave completely destructively interferes with itself
    • A system is driven at its natural frequency, producing a large amplitude increase
    • Two waves travel through each other unaffected
    • A wave reflects off a fixed boundary

    Resonance is a dramatic amplitude increase that occurs when a driving frequency matches a system's natural frequency.

  15. A wave's amplitude is doubled. Its wave speed:

    • Doubles
    • Quadruples
    • Stays the same, since speed depends on the medium
    • Is halved

    Wave speed depends only on the properties of the medium, not amplitude or frequency.

Unit 6: Electricity (16)
  1. Two point charges of +2 μC and +3 μC are separated by 0.1 m. What is the electric force between them (k=8.99×10⁹ N·m²/C²)?

    • Approximately 5.4 N
    • Approximately 54 N
    • Approximately 0.54 N
    • Approximately 540 N

    Fe = kq1q2/r² = (8.99×10⁹)(2×10⁻⁶)(3×10⁻⁶)/(0.1²) = (8.99×10⁹)(6×10⁻¹²)/0.01 ≈ 5.39 N.

  2. If the distance between two charges is halved, the electric force between them becomes:

    • Half as strong
    • Twice as strong
    • 4 times as strong
    • 1/4 as strong

    Coulomb's law is inverse-square: halving r increases force by a factor of (1/0.5)²=4.

  3. Electric field lines around an isolated positive charge point:

    • Toward the charge
    • Away from the charge
    • In circles around the charge
    • In random directions

    Field lines point away from positive charges (the direction a positive test charge would be pushed) and toward negative charges.

  4. A resistor has V=12 V across it and carries I=3 A. What is its resistance?

    • 4 Ω
    • 36 Ω
    • 0.25 Ω
    • 15 Ω

    R = V/I = 12/3 = 4 Ω.

  5. Three 2 Ω resistors are connected in series. What is the total resistance?

    • 2 Ω
    • 0.67 Ω
    • 6 Ω
    • 8 Ω

    Series resistances add directly: Rtotal = 2+2+2 = 6 Ω.

  6. Three 6 Ω resistors are connected in parallel. What is the total resistance?

    • 18 Ω
    • 6 Ω
    • 2 Ω
    • 0.5 Ω

    1/Rtotal = 1/6+1/6+1/6 = 3/6 = 1/2, so Rtotal = 2 Ω.

  7. In a series circuit with two resistors, which quantity is the same through both resistors?

    • Voltage
    • Current
    • Power
    • Resistance

    In a series circuit, there's only one path, so the current is identical through every component.

  8. In a parallel circuit, which quantity is the same across every branch?

    • Current
    • Resistance
    • Voltage
    • Power

    Each parallel branch connects across the same two nodes, so voltage is identical across all branches.

  9. A circuit has a 12 V source and total resistance of 4 Ω. What is the total current?

    • 3 A
    • 48 A
    • 0.33 A
    • 16 A

    I = V/R = 12/4 = 3 A.

  10. A device draws 2 A at 120 V. What power does it consume?

    • 60 W
    • 240 W
    • 122 W
    • 0.017 W

    P = IV = (2)(120) = 240 W.

  11. If one bulb burns out (opens) in a series string of holiday lights, what happens to the rest of the string?

    • The rest stay lit normally
    • The rest also go out, since the circuit is broken
    • The rest get brighter
    • Nothing changes

    In a series circuit there's only one current path; if it's broken anywhere, no current flows anywhere in the loop.

  12. If one branch fails (opens) in a parallel circuit, what happens to the other branches?

    • They stop working too
    • They continue to operate normally
    • They short-circuit
    • Voltage across them becomes zero

    Parallel branches are independent paths; if one opens, current can still flow through the remaining branches.

  13. Which of the following increases the resistance of a wire?

    • Increasing its cross-sectional area
    • Increasing its length
    • Decreasing its length
    • Decreasing its resistivity

    R = ρL/A — resistance increases directly with length and decreases with cross-sectional area.

  14. What is the SI unit of electric charge?

    • Ampere
    • Volt
    • Coulomb
    • Ohm

    The coulomb (C) is the SI unit of electric charge.

  15. A charge of 4 C flows past a point in a wire in 2 seconds. What is the current?

    • 8 A
    • 2 A
    • 0.5 A
    • 6 A

    I = q/t = 4/2 = 2 A.

  16. Doubling the voltage across a fixed resistor does what to the power dissipated?

    • Doubles it
    • Quadruples it
    • Halves it
    • No change

    P = V²/R, so doubling V quadruples P (for constant R).

Unit 7: Magnetism & Electromagnetism (15)
  1. Which statement about magnetic poles is correct?

    • Isolated magnetic monopoles have been observed in labs
    • Like poles attract and opposite poles repel
    • Like poles repel and opposite poles attract
    • Magnets only have a single pole

    As with electric charges, like magnetic poles repel and opposite poles attract; monopoles have never been observed.

  2. Outside a bar magnet, magnetic field lines point:

    • From south to north
    • From north to south
    • In random directions
    • Only inward, toward the center

    Outside the magnet, field lines emerge from the north pole and enter the south pole, forming closed loops through the magnet's interior.

  3. A charged particle moves parallel to a magnetic field. What magnetic force does it experience?

    • Maximum force
    • Zero force
    • Force perpendicular to both v and B, of medium size
    • Force equal to qvB

    F = qvB sinθ; when θ=0° (parallel), sinθ=0, so the force is zero.

  4. A charged particle moves perpendicular to a magnetic field. What is the shape of its resulting path?

    • A straight line
    • A parabola
    • A circle
    • An ellipse

    The magnetic force is always perpendicular to velocity, continuously changing direction without changing speed — producing uniform circular motion.

  5. The magnetic force on a moving charge does what to its kinetic energy?

    • Increases it
    • Decreases it
    • Leaves it unchanged, since the force is always perpendicular to velocity
    • Doubles it instantly

    Since F is always perpendicular to v, it does no work on the charge, so kinetic energy (and speed) stays constant.

  6. What is required to induce an EMF in a loop of wire via electromagnetic induction?

    • A strong, constant magnetic field through the loop
    • A changing magnetic flux through the loop
    • A stationary magnet near the loop
    • Any magnetic field, changing or not

    Faraday's Law requires a CHANGING magnetic flux — a constant field through a stationary loop induces nothing.

  7. According to Lenz's Law, an induced current flows in a direction that:

    • Increases the change in flux that caused it
    • Opposes the change in flux that caused it
    • Has no relationship to the change in flux
    • Is always clockwise

    Lenz's Law: induced current opposes the change in magnetic flux, consistent with conservation of energy.

  8. A generator converts:

    • Electrical energy to mechanical energy
    • Mechanical energy to electrical energy
    • Chemical energy to electrical energy
    • Electrical energy to chemical energy

    A generator uses mechanical motion (rotating a coil in a magnetic field) to induce an EMF — converting mechanical to electrical energy.

  9. A motor converts:

    • Electrical energy to mechanical energy
    • Mechanical energy to electrical energy
    • Thermal energy to electrical energy
    • Light energy to electrical energy

    A motor uses current in a magnetic field to produce a force (torque), converting electrical energy into mechanical motion.

  10. A wire carrying current I=5 A, of length 0.4 m, sits perpendicular to a magnetic field of 0.2 T. What force does it experience?

    • 0.4 N
    • 4 N
    • 1 N
    • 0.04 N

    F=BIL sinθ = (0.2)(5)(0.4)(sin90°) = 0.4 N.

  11. Increasing the number of turns in a coil used for electromagnetic induction:

    • Decreases the induced EMF
    • Has no effect on the induced EMF
    • Increases the induced EMF
    • Reverses the polarity only

    More turns means the changing flux links more loops, increasing the total induced EMF.

  12. The direction of the magnetic field around a straight current-carrying wire is found using:

    • Snell's Law
    • The right-hand rule
    • Ohm's Law
    • Kepler's Law

    The right-hand rule: point the thumb along conventional current, and the curled fingers show the direction of the circular magnetic field.

  13. A magnet is pushed into a stationary coil of wire, inducing a current. If the magnet is pushed in faster, the induced EMF:

    • Decreases
    • Stays the same
    • Increases
    • Becomes zero

    Faster motion means a faster rate of change of flux, which increases the induced EMF (Faraday's Law).

  14. Why do AC generators produce alternating (rather than direct) current?

    • Because the wire resistance alternates
    • Because the coil's orientation relative to the magnetic field continuously changes as it rotates
    • Because of random electron motion
    • Because the magnetic field alternates on its own

    As the coil rotates, the rate and direction of flux change through it varies sinusoidally, producing an alternating induced EMF.

  15. Which of the following experiences zero magnetic force in a magnetic field?

    • A charge moving perpendicular to the field
    • A stationary charge
    • A charge moving at an angle to the field
    • A current-carrying wire perpendicular to the field

    Magnetic force depends on velocity (F=qvB sinθ); a stationary charge (v=0) experiences no magnetic force.

Unit 8: Optics (15)
  1. A light ray strikes a plane mirror at 30° from the normal. At what angle does it reflect?

    • 30° from the normal
    • 60° from the normal
    • 30° from the mirror surface

    Law of reflection: angle of incidence = angle of reflection, both measured from the normal, so it reflects at 30° from the normal.

  2. A plane mirror image is:

    • Real, inverted, magnified
    • Virtual, upright, same size as the object
    • Real, upright, reduced
    • Virtual, inverted, magnified

    A flat (plane) mirror always forms a virtual, upright, same-size image located as far behind the mirror as the object is in front.

  3. Light travels from air (n=1.00) into glass (n=1.50). It will bend:

    • Away from the normal
    • Toward the normal
    • Not at all
    • Parallel to the surface

    Light bends toward the normal when entering a medium with a higher index of refraction (denser, slower light speed).

  4. Light in water (n=1.33) hits the water-air boundary at an angle greater than the critical angle. What happens?

    • It refracts into the air as normal
    • Total internal reflection occurs — all light reflects back into the water
    • The light is absorbed
    • The light splits into a rainbow

    Beyond the critical angle, going from a denser to less dense medium, total internal reflection occurs — no light exits.

  5. Using Snell's Law, light passes from a medium with n1=1.5 into a medium with n2=1.0, hitting the boundary at 30° from the normal. Which best describes the refracted angle?

    • Less than 30°, bending toward the normal
    • Greater than 30°, bending away from the normal
    • Exactly 30°, no bending
    • The light cannot refract

    n1sinθ1=n2sinθ2 → since n2<n1, sinθ2 must be larger than sinθ1, so θ2>30° — light bends away from the normal entering a less dense medium.

  6. A convex (converging) lens forms what kind of image when the object is placed beyond the focal point?

    • Virtual and upright
    • Real and inverted
    • Virtual and inverted
    • No image forms

    When do>f for a converging lens, light rays converge on the far side, forming a real, inverted image.

  7. An object is placed inside the focal length of a convex lens (do<f). The resulting image is:

    • Real, inverted, reduced
    • Virtual, upright, magnified
    • Real, upright, magnified
    • Virtual, inverted, reduced

    When the object is closer than the focal point, the lens acts as a magnifying glass, producing a virtual, upright, magnified image.

  8. An object is placed 30 cm from a convex lens with a focal length of 10 cm. Using 1/f=1/do+1/di, what is the image distance?

    • 7.5 cm
    • 15 cm
    • 20 cm
    • 30 cm

    1/di = 1/f − 1/do = 1/10 − 1/30 = 3/30 − 1/30 = 2/30 = 1/15, so di = 15 cm.

  9. A convex mirror (like a car's passenger side mirror) always forms an image that is:

    • Real, inverted, magnified
    • Virtual, upright, reduced
    • Real, upright, same size
    • Virtual, inverted, magnified

    Convex (diverging) mirrors always produce virtual, upright, reduced images, giving a wider field of view.

  10. Which type of lens or mirror can form a REAL image?

    • Convex (diverging) lens only
    • Convex (diverging) mirror only
    • Concave (converging) mirror, if the object is beyond the focal point
    • Any lens or mirror, regardless of type

    Only converging elements (convex lens, concave mirror) can produce real images, and only when the object is beyond the focal point.

  11. What is the index of refraction of a medium in which light travels at 2.0×10⁸ m/s (c=3.0×10⁸ m/s)?

    • 0.67
    • 1.5
    • 1.0
    • 2.0

    n = c/v = (3.0×10⁸)/(2.0×10⁸) = 1.5.

  12. Which best explains why a straw appears bent at the water's surface when viewed from the side?

    • Reflection
    • Diffraction
    • Refraction — light bends as it passes from water into air
    • Total internal reflection

    Refraction bends light rays as they cross the water-air boundary due to the change in speed, making the submerged part of the straw appear displaced/bent.

  13. A magnification of m=−2 for an image means:

    • The image is upright and twice the size
    • The image is inverted and twice the size
    • The image is upright and half the size
    • The image is inverted and half the size

    A negative m indicates an inverted image; the magnitude (2) means the image is twice the height of the object.

  14. Diffuse reflection occurs because:

    • The surface is perfectly smooth
    • The surface is rough, scattering parallel rays in many directions
    • Light is absorbed and re-emitted
    • The angle of incidence is zero

    A rough surface reflects parallel incoming rays at many different angles (still following the law of reflection at each microscopic point), preventing a clear image from forming.

  15. The critical angle for total internal reflection depends on:

    • The wavelength of light only
    • The ratio of the two media's indices of refraction
    • The intensity of the light
    • The size of the object

    sinθc = n2/n1, so the critical angle depends on the ratio of the refractive indices of the two media.

Unit 9: Modern Physics (16)
  1. In the photoelectric effect, increasing the intensity of light above the threshold frequency mainly increases:

    • The maximum kinetic energy of ejected electrons
    • The number of ejected electrons
    • The threshold frequency
    • The work function of the metal

    Intensity relates to the number of photons hitting the metal per second, which increases the number (rate) of ejected electrons, not their individual energy.

  2. In the photoelectric effect, increasing the frequency of light (above threshold) mainly increases:

    • The number of ejected electrons
    • The maximum kinetic energy of ejected electrons
    • The metal's work function
    • The threshold frequency

    Each photon's energy is E=hf; higher frequency means each photon carries more energy, increasing the max KE of ejected electrons (KEmax=hf−W0).

  3. A metal has a work function of 2.0 eV. Light with photon energy 3.0 eV strikes it. What is the maximum kinetic energy of an ejected electron?

    • 5.0 eV
    • 1.0 eV
    • 2.0 eV
    • 3.0 eV

    KEmax = hf − W0 = 3.0 − 2.0 = 1.0 eV.

  4. Light striking a metal below its threshold frequency, no matter how intense, will:

    • Eject electrons with high kinetic energy
    • Eject many electrons but with low kinetic energy
    • Eject no electrons at all
    • Eject electrons only after a time delay

    Below the threshold frequency, individual photons don't carry enough energy to overcome the work function, so no electrons are ejected regardless of intensity.

  5. The de Broglie wavelength of a particle is given by:

    • λ = hf
    • λ = h/p
    • λ = hc
    • λ = pc/h

    De Broglie's relation: λ = h/p = h/(mv), describing the wave nature of matter.

  6. Which experiment provides strong evidence for the wave nature of light?

    • The photoelectric effect
    • Double-slit diffraction/interference
    • Compton scattering
    • Radioactive decay

    Double-slit diffraction and interference patterns are classic evidence of light's wave nature; the photoelectric effect instead evidences light's particle nature.

  7. In the Bohr model, an atom emits a photon when:

    • An electron absorbs energy and jumps to a higher level
    • An electron falls from a higher to a lower energy level
    • The nucleus captures an electron
    • Two atoms collide elastically

    A photon is emitted when an electron transitions from a higher to a lower allowed energy level, releasing energy equal to the level difference.

  8. Bright-line emission spectra are unique to each element because:

    • Each element has the exact same energy levels
    • Each element has its own unique set of quantized electron energy levels
    • Bright-line spectra are actually identical for all elements
    • Emission spectra depend only on temperature

    Each element has a distinct set of quantized energy levels, so the photon energies (and thus wavelengths) it can emit/absorb form a unique 'fingerprint.'

  9. Which particle is emitted in alpha decay?

    • An electron
    • A helium nucleus (2 protons + 2 neutrons)
    • A photon
    • A neutron only

    Alpha decay emits an alpha particle, which is a helium-4 nucleus (2 protons, 2 neutrons).

  10. After an alpha decay, the mass number and atomic number of the parent nucleus change by:

    • Mass number −4, atomic number −2
    • Mass number −2, atomic number −4
    • Mass number unchanged, atomic number −2
    • Mass number −4, atomic number unchanged

    Alpha decay removes 2 protons and 2 neutrons, so mass number decreases by 4 and atomic number decreases by 2.

  11. Which type of radioactive decay is stopped by just a sheet of paper?

    • Alpha
    • Beta
    • Gamma
    • All types equally

    Alpha particles have the least penetrating power (but highest ionizing power) and are stopped by paper or skin.

  12. Which type of radioactive decay requires lead or thick concrete to stop?

    • Alpha
    • Beta
    • Gamma
    • None; all pass through lead

    Gamma rays are high-energy photons with the greatest penetrating power, requiring dense shielding like lead or thick concrete.

  13. A radioactive sample has a half-life of 4 days. After 12 days, what fraction of the original sample remains?

    • 1/2
    • 1/4
    • 1/8
    • 1/16

    12 days = 3 half-lives, so the remaining fraction is (1/2)³ = 1/8.

  14. Nuclear fusion, the process that powers the Sun, involves:

    • Splitting a heavy nucleus into smaller nuclei
    • Combining light nuclei into a heavier nucleus, releasing energy
    • Emitting only gamma rays with no nuclear change
    • Converting an electron into a proton

    Fusion combines light nuclei (e.g., hydrogen into helium), releasing a large amount of energy — the process that powers stars.

  15. According to mass-energy equivalence, a small amount of mass converted entirely to energy releases:

    • A negligible amount of energy
    • An amount of energy given by E=mc², which is very large due to c²
    • Energy only in the form of heat
    • No energy; mass and energy are unrelated

    E=mc² shows that even a tiny mass corresponds to an enormous amount of energy because c² (≈9×10¹⁶ m²/s²) is such a large number.

  16. Beta decay involves:

    • Emission of a helium nucleus
    • A neutron converting to a proton (or vice versa), emitting an electron or positron
    • Emission of a high-energy photon with no change in atomic number
    • Splitting of the nucleus into two roughly equal parts

    In beta-minus decay, a neutron converts to a proton and an electron (beta particle) is emitted; atomic number increases by 1, mass number stays the same.

Term
Definition
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Unit 1: Kinematics

Displacement
Vector change in position, Δx = xf − xi. Can be zero even after a long trip if you return to start.
Distance
Scalar total path length traveled; always ≥ magnitude of displacement.
Instantaneous velocity
The slope of the tangent line to a position-time graph at one instant.
Acceleration
Vector rate of change of velocity, a = Δv/Δt. Occurs whenever speed OR direction changes.
Free fall acceleration (g)
9.8 m/s² downward near Earth's surface, same for all masses (ignoring air resistance).
Kinematic equation (no x term)
vf = vi + at
Kinematic equation (no vf term)
Δx = vi·t + ½at²
Kinematic equation (no t term)
vf² = vi² + 2aΔx
Projectile motion
Horizontal velocity stays constant; vertical velocity changes due to gravity — the two directions are independent.

Unit 2: Newton's Laws & Dynamics

Newton's First Law
An object at rest or in constant-velocity motion stays that way unless acted on by a net external force (inertia).
Newton's Second Law
Fnet = ma — acceleration is proportional to net force and inversely proportional to mass.
Newton's Third Law
For every action force, there's an equal and opposite reaction force acting on a DIFFERENT object.
Normal force
Contact force perpendicular to a surface, preventing objects from passing through each other.
Static friction
Friction that resists the START of sliding; maximum value fs,max = μs·FN.
Kinetic friction
Friction that resists sliding once motion has begun: fk = μk·FN.
Free-body diagram
A diagram isolating one object, showing every external force acting on it as an arrow.
Weight
The gravitational force on an object, Fg = mg — not the same as mass.

Unit 3: Momentum & Energy

Momentum
p = mv, a vector describing an object's quantity of motion.
Impulse
J = FΔt = Δp — the change in momentum caused by a force acting over time.
Conservation of momentum
In an isolated system, total momentum before an interaction equals total momentum after.
Elastic collision
Momentum AND kinetic energy are both conserved; objects bounce apart without permanent deformation.
Inelastic collision
Momentum is conserved, but kinetic energy is not — some converts to heat/sound/deformation.
Work
W = Fd cosθ — energy transferred by a force acting through a displacement.
Work-energy theorem
The net work done on an object equals its change in kinetic energy: Wnet = ΔKE.
Kinetic energy
KE = ½mv² — energy of motion, always non-negative.
Conservation of mechanical energy
KEi + PEi = KEf + PEf when only conservative forces (gravity, springs) act on the system.

Unit 4: Circular Motion & Gravitation

Centripetal acceleration
ac = v²/r, always directed toward the center of a circular path.
Centripetal force
Fc = mv²/r — the net inward force needed for circular motion, supplied by tension, gravity, friction, or normal force.
Universal gravitation
Fg = Gm1m2/r² — attractive force between any two masses, inverse-square with distance.
Kepler's Third Law
T² ∝ r³ — orbital period squared is proportional to orbital radius cubed.
Orbital speed
v = √(Gm1/r) — depends on the central mass and orbital radius, not the satellite's own mass.
Circular motion speed
v = 2πr/T — speed of an object moving in a circle of radius r with period T.
Kepler's First Law
Planets orbit the Sun in ellipses, with the Sun at one focus.
Kepler's Second Law
A line from the Sun to a planet sweeps out equal areas in equal times — planets move faster near the Sun.
Gravitational constant G
6.67×10⁻¹¹ N·m²/kg² — the proportionality constant in Newton's law of universal gravitation.

Unit 5: Waves & Sound

Wavelength
Distance between two successive identical points on a wave (e.g., crest to crest).
Frequency
Number of complete wave cycles per second, measured in hertz (Hz).
Wave speed equation
v = fλ — determined by the medium, not by frequency or amplitude alone.
Transverse wave
Particles vibrate perpendicular to the direction of energy travel (e.g., light, waves on a string).
Longitudinal wave
Particles vibrate parallel to the direction of energy travel, with compressions and rarefactions (e.g., sound).
Constructive interference
In-phase waves add together, producing a larger amplitude.
Doppler effect
Apparent shift in observed frequency due to relative motion between a wave source and observer.

Unit 6: Electricity

Coulomb's Law
Fe = kq1q2/r² — the electric force between two point charges, inverse-square with distance.
Electric field
E = F/q — force per unit positive test charge; points away from + charges, toward − charges.
Ohm's Law
V = IR — relates voltage, current, and resistance.
Series circuit
Same current everywhere; total resistance = sum of individual resistances.
Parallel circuit
Same voltage across every branch; total resistance is less than the smallest individual resistor.
Electric power
P = IV = I²R = V²/R — rate of electrical energy transfer.
Charge quantization
Charge is quantized: q = ne, where e = 1.6×10⁻¹⁹ C is the elementary charge.
Conservation of charge
Total charge in an isolated system is constant — charge is transferred, never created or destroyed.
Resistivity
A material property in R = ρL/A; resistance increases with length, decreases with cross-sectional area.

Unit 7: Magnetism & Electromagnetism

Magnetic force on a moving charge
F = qvB sinθ — zero if velocity is parallel to the field, maximum if perpendicular.
Right-hand rule
Used to find the direction of a magnetic field around a current, or the force on a moving charge in a field.
Faraday's Law
A changing magnetic flux through a loop induces an EMF (voltage) in that loop.
Lenz's Law
Induced current flows in a direction that opposes the change in flux that created it.
Force on a current-carrying wire
F = BIL sinθ — the magnetic force on a wire of length L carrying current I in field B.
Motor
Converts electrical energy to mechanical energy using the force on a current-carrying coil in a magnetic field.
Generator
Converts mechanical energy to electrical energy by rotating a coil within a magnetic field, inducing an EMF.

Unit 8: Optics

Law of reflection
Angle of incidence equals angle of reflection, both measured from the normal.
Index of refraction
n = c/v — ratio of light's speed in a vacuum to its speed in a medium; always ≥ 1.
Snell's Law
n1 sinθ1 = n2 sinθ2 — relates the bending of light at a boundary between two media.
Total internal reflection
Occurs when light travels from a denser to less dense medium beyond the critical angle — all light reflects, none refracts out.
Convex (converging) lens
Thicker in the middle; focuses parallel rays to a real focal point.
Thin lens equation
1/f = 1/do + 1/di — relates focal length, object distance, and image distance.

Unit 9: Modern Physics

Photoelectric effect
Light above a threshold frequency ejects electrons from a metal; explained by treating light as photons, E = hf.
Work function
W0 — the minimum energy needed to eject an electron from a metal's surface.
De Broglie wavelength
λ = h/p — matter waves; all moving matter has an associated wavelength.
Half-life
The time for half of a radioactive sample to decay; decay is exponential, not linear.
Alpha decay
Nucleus emits a helium nucleus (2p+2n); mass number −4, atomic number −2; stopped by paper.
Gamma decay
Nucleus emits high-energy EM radiation; no change in mass or atomic number; needs lead/concrete to stop.
Beta decay
A neutron converts to a proton (emitting an electron); mass number unchanged, atomic number ±1; stopped by aluminum.
Nuclear fusion
Combining light nuclei into a heavier one, releasing large amounts of energy — powers the Sun.

Core Formulas

Kinematics 1
vf = vi + at
Kinematics 2
Δx = vi·t + ½at²
Kinematics 3
vf² = vi² + 2aΔx
Kinematics 4
Δx = ½(vi+vf)t
Newton's 2nd Law
Fnet = ma
Weight
Fg = mg
Friction
ff = μFN
Momentum
p = mv
Impulse
J = FΔt = Δp
Work
W = Fd cosθ
Kinetic Energy
KE = ½mv²
Grav. PE
PE = mgh
Spring PE
PE = ½kx²
Power
P = W/t = Fv
Centripetal Accel.
ac = v²/r
Centripetal Force
Fc = mv²/r
Universal Gravitation
Fg = Gm₁m₂/r²
Kepler's 3rd Law
T² ∝ r³
Wave Speed
v = fλ
Frequency/Period
f = 1/T
Coulomb's Law
Fe = kq₁q₂/r²
Electric Field
E = F/q
Ohm's Law
V = IR
Electric Power
P = IV = I²R = V²/R
Magnetic Force (charge)
F = qvB sinθ
Magnetic Force (wire)
F = BIL sinθ
Index of Refraction
n = c/v
Snell's Law
n₁sinθ₁ = n₂sinθ₂
Thin Lens/Mirror
1/f = 1/do + 1/di
Magnification
m = −di/do = hi/ho
Photon Energy
E = hf
Photoelectric Effect
KEmax = hf − W0
De Broglie Wavelength
λ = h/p
Mass-Energy Equivalence
E = mc²

Physical Constants

ConstantSymbolValue
Acceleration due to gravityg9.8 m/s²
Universal gravitation constantG6.67×10⁻¹¹ N·m²/kg²
Coulomb's constantk8.99×10⁹ N·m²/C²
Elementary chargee1.6×10⁻¹⁹ C
Planck's constanth6.63×10⁻³⁴ J·s
Speed of light in vacuumc3.0×10⁸ m/s
Speed of sound in air (room temp)v≈343 m/s

Radioactive Decay Types

Decay TypeEmittedMass # ChangeAtomic # ChangePenetration
Alpha (α)⁴₂He nucleus−4−2Stopped by paper (least penetrating, most ionizing)
Beta⁻ (β⁻)⁰₋₁e (electron)0+1Stopped by aluminum
Positron (β⁺)⁰₊₁e0−1Stopped by aluminum
Gamma (γ)⁰₀γ (photon)00Needs lead/concrete (most penetrating, least ionizing)

Half-Life Reference Table

# Half-LivesFraction Left% Remaining% Decayed
01100%0%
11/250%50%
21/425%75%
31/812.5%87.5%
41/166.25%93.75%
51/323.125%96.875%

Series vs Parallel Circuits

PropertySeriesParallel
CurrentSame through every componentDivides among branches
VoltageDivides across componentsSame across every branch
Total resistanceRtotal = R1+R2+...1/Rtotal = 1/R1+1/R2+... (< smallest R)
If one component fails (opens)Entire circuit stopsOther branches keep working

Electromagnetic Spectrum (low → high energy)

RegionRelative WavelengthRelative Frequency/Energy
RadioLongestLowest
MicrowaveLongLow
InfraredMedium-longMedium-low
Visible (ROYGBIV)MediumMedium
UltravioletMedium-shortMedium-high
X-rayShortHigh
GammaShortestHighest

Lens & Mirror Sign Conventions

  1. Converging (convex lens / concave mirror): f is positive.
  2. Diverging (concave lens / convex mirror): f is negative.
  3. Real image: di is positive; can be projected onto a screen.
  4. Virtual image: di is negative; cannot be projected onto a screen.
  5. Upright image: magnification m is positive.
  6. Inverted image: magnification m is negative.
  7. A converging lens/mirror forms a real image only when the object is beyond the focal point (do > f).
  8. A diverging lens/mirror ALWAYS forms a virtual, upright, reduced image, regardless of object distance.

Exam Day Checklist

  • Write down every given value with its units before starting a calculation.
  • Choose the correct kinematic equation based on which variable is missing.
  • Draw a free-body diagram before applying Newton's Second Law.
  • For circular motion, remember the centripetal force is supplied by a real force — identify which one.
  • Check whether a collision is elastic or inelastic before assuming kinetic energy is conserved.
  • In circuits, identify series vs. parallel sections before computing total resistance.
  • Use the right-hand rule carefully for magnetic field and force direction problems.
  • For optics, determine real/virtual and upright/inverted using sign conventions, not guesswork.
  • Track units all the way through a calculation — mismatched units signal an error.
  • Double-check sig figs and rounding only in the final answer, not intermediate steps.
Quick ways to lock in the facts you keep forgetting. Read the big trick, then the small note tells you what it unlocks. Say them out loud — silly is memorable.

Kinematics

Same sign, speeding; opposite, slowing
If velocity and acceleration have the same sign, the object speeds up. Opposite signs mean it's slowing down — direction alone doesn't tell you.
No time? No place? Pick the matching equation
Each kinematic equation is missing exactly one variable — vf=vi+at skips Δx, Δx=vit+½at² skips vf, vf²=vi²+2aΔx skips t. Match what's missing to what you don't have.
Top of the toss, still falling
At the peak of a thrown ball's path, velocity is zero but acceleration is still −g. Zero velocity does NOT mean zero acceleration.
Sideways and downways don't talk
In projectile motion, horizontal and vertical motions are totally independent — horizontal velocity never changes, vertical acceleration is always −g.

Newton's Laws & Forces

Third law pairs never meet on one object
Action-reaction forces act on two DIFFERENT objects, so they can never cancel each other out on the same free-body diagram.
Mass is yours everywhere, weight isn't
Mass (kg) never changes with location. Weight (N) = mg changes wherever gravity changes — that's why you'd weigh less on the Moon but have the same mass.
Friction depends on push-down, not push-across
Friction force = μ×FN depends on how hard surfaces press together (normal force), never on the contact area.
Constant velocity means balanced, not motionless
Zero NET force means constant velocity, which includes rest — but also includes cruising at any constant speed in a straight line.

Momentum & Energy

Momentum always survives, energy sometimes doesn't
Momentum is conserved in EVERY collision. Kinetic energy is only conserved in elastic collisions — inelastic ones lose some to heat/sound.
Perpendicular force does nothing
If a force is at 90° to the displacement, W = Fd cos90° = 0. Carrying a bag level, or moving in a circle — no work is done.
Double the speed, quadruple the energy
KE = ½mv² depends on velocity SQUARED — doubling speed doesn't double kinetic energy, it quadruples it.
Longer time, softer hit
Airbags and padding stretch out the time of impact for the same impulse (Δp), which lowers the force (J=FΔt) and reduces injury.

Circular Motion & Gravity

Centripetal isn't its own force — it's a job title
"Centripetal force" just describes the inward net force — it's actually supplied by tension, gravity, friction, or normal force, never a separate force type.
There's no real push outward
The "flung outward" feeling in a turning car is just your own inertia resisting the turn — there is no real outward (centrifugal) force acting on you.
Double the distance, quarter the pull
Gravity (and Coulomb's law) follow inverse-square laws — doubling distance cuts the force to 1/4, not 1/2.
Farther out, slower orbit
A satellite in a bigger orbit moves slower (v=√(GM/r)) — and its own mass doesn't matter at all.

Waves & Sound

The medium sets the speed limit
Wave speed (v=fλ) depends on the medium only. Change the frequency and wavelength adjusts to compensate — speed doesn't budge.
No stuff, no sound
Sound needs particles to compress and rarefy, so it can't cross a vacuum. Light doesn't need a medium — that's the key difference.
Toward you = squeezed = higher pitch
Doppler effect: a source moving toward you compresses wavefronts (higher perceived pitch); moving away stretches them (lower pitch) — the source's own frequency never changes.

Electricity

Series shares current, parallel shares voltage
In series, the SAME current flows through everything. In parallel, the SAME voltage sits across every branch. Never mix these up.
Parallel resistance always shrinks
Adding a parallel branch gives current another path, so total resistance always drops BELOW the smallest single resistor.
Electric force swings both ways
Unlike gravity (always attractive), Coulomb force can push or pull — like charges repel, opposite charges attract.

Magnetism

Parallel to the field means zero force
F=qvB sinθ — if a charge moves parallel to B (θ=0°), sinθ=0 and the magnetic force vanishes.
No monopoles, ever
You can never isolate just a north or south pole — cut a magnet in half and you get two smaller magnets, each with both poles.
No change, no current
Electromagnetic induction needs a CHANGING magnetic flux — a stationary loop sitting in a constant field induces absolutely nothing.

Optics

Denser bends it in, thinner bends it out
Light bends TOWARD the normal entering a denser (higher-n) medium, and AWAY from the normal entering a thinner one.
Convex mirrors never lie big
A convex (diverging) mirror always makes a virtual, upright, SMALLER image — no exceptions, regardless of object distance.
Real flips it, virtual doesn't
Real images (projectable on a screen) from a single lens or mirror are always inverted. Virtual images are always upright.

Modern Physics

Intensity = more electrons, frequency = stronger electrons
In the photoelectric effect, brighter light ejects MORE electrons; higher-frequency light ejects FASTER (higher-KE) electrons — two different jobs.
Alpha's heavy and slow, gamma's light and fast
Alpha particles are big, stopped by paper, but very ionizing. Gamma rays are pure energy, pass through almost anything, but ionize the least.
Half of what's left, every half-life
Half-life always removes half of whatever remains — it's exponential decay, never a constant number of atoms per unit time.
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