AP Physics 1 Study Guide

Unit 1: Kinematics

Displacement

The vector change in position, Δx = $x_f − x_i$; depends only on initial and final points, not the path taken.

Instantaneous Velocity

The slope of the tangent line to a position-time graph at a specific instant; the derivative of position with respect to time.

Acceleration

The rate of change of velocity with respect to time, a = Δv/Δt, measured in m/s².

Kinematic Equation: v = v₀ + at

Relates final velocity to initial velocity, constant acceleration, and time; used when displacement is not needed.

Kinematic Equation: Δx = v₀t + ½at²

Gives displacement in terms of initial velocity, constant acceleration, and time.

Free Fall

Motion under gravity alone, with constant downward acceleration g = 9.8 m/s², independent of the object's mass.

Projectile Motion

Two-dimensional motion with constant horizontal velocity and constant vertical acceleration (−g), analyzed by treating each axis independently.

Range of a Projectile

R = v₀²sin(2θ)/g for equal launch and landing heights; maximized at a launch angle of 45°.

Position-Time Graph

A graph where the slope at any point equals the instantaneous velocity; a parabolic shape indicates constant acceleration.

Velocity-Time Graph

A graph where the slope equals acceleration and the area under the curve equals displacement.

Unit 2: Dynamics & Newton's Laws

Newton's First Law

An object at rest stays at rest, and an object in motion stays in motion at constant velocity, unless acted on by a net external force.

Newton's Second Law

ΣF = ma; the net force on an object equals the product of its mass and acceleration, with acceleration in the direction of net force.

Newton's Third Law

For every action force one object exerts on another, the second object exerts an equal and opposite force back on the first.

Normal Force

The perpendicular contact force a surface exerts on an object, preventing it from passing through the surface; not always equal to weight.

Static Friction

The force resisting the start of sliding between surfaces in contact, with maximum value $f_s$(max) = $μ_s$ N.

Kinetic Friction

The force opposing relative sliding motion between two surfaces, given by $f_k = μ_k$ N, generally less than max static friction.

Tension

The pulling force transmitted through a string, rope, or cable; uniform throughout an ideal massless string over a frictionless pulley.

Free-Body Diagram

A diagram showing all external forces acting on a single object as vectors, used to apply Newton's Second Law systematically.

Apparent Weight

The normal force experienced by an object, which differs from true weight (mg) when the object has vertical acceleration, such as in an elevator.

Inclined Plane Decomposition

Gravity on an incline splits into components mg sinθ (along the slope) and mg cosθ (perpendicular to the slope, balanced by normal force).

Unit 3: Circular Motion & Gravity

Centripetal acceleration

$a_c = v^2/r = omega^2$ r; always points toward the center of the circular path, even at constant speed.

Centripetal force

$F_c = mv^2/r$, the net inward force supplied by real forces (tension, gravity, friction, normal force) that causes circular motion.

Newton's Law of Universal Gravitation

$F_g$ = Gm1m2/$r^2$, where G = 6.674x10^-11 N*$m^2/kg^2$; always attractive, acts along the line joining the masses.

Orbital speed

v = $sqrt{GM/r}$ for a circular orbit, derived by setting gravity equal to the required centripetal force.

Kepler's Third Law

$T^2$ is proportional to $r^3$ for all objects orbiting the same central body.

Gravitational potential energy

$U_g$ = -GMm/r, taken as zero at infinite separation; always negative for a bound system.

Escape velocity

$v_{esc} = sqrt{2GM/r}$, the minimum launch speed needed to escape a gravitational field from radius r.

Minimum speed at top of a vertical loop

$v_{min} = sqrt{gr}$, the speed at which normal force drops to zero and gravity alone supplies centripetal force.

Angular velocity (omega)

omega = v/r = 2*pi*f, the rate of angular rotation in radians per second; relates to linear speed via v = omega*r.

Banked curve

On a frictionless banked curve, a component of the normal force provides centripetal force: tan(theta) = $v^2$/(rg).

Unit 4: Rotational Motion

Torque

tau = rF*sin(theta), the rotational analogue of force; measures how effectively a force causes angular acceleration about a pivot.

Moment of inertia

I = sum(m*$r^2$); the rotational analogue of mass, depending on both mass and its distribution relative to the rotation axis.

Rotational Newton's Second Law

Net torque equals moment of inertia times angular acceleration: sum(tau) = I*alpha.

Angular momentum

L = I*omega for a rigid body; conserved when net external torque on a system is zero.

Parallel axis theorem

I = $I_{cm} + M$*$d^2$, used to find moment of inertia about an axis parallel to one through the center of mass, a distance d away.

Rotational kinetic energy

$KE_{rot}$ = (1/2)*I*$omega^2$, the kinetic energy stored in a rotating object.

Rolling without slipping condition

$v_{cm}$ = omega*r and $a_{cm}$ = alpha*r; static friction (not kinetic) allows rolling without energy loss.

Moment of inertia of a solid disk/cylinder

I = (1/2)*M*$R^2$ about its central axis.

Conservation of angular momentum example

A spinning skater pulling arms inward decreases I, so omega increases to keep L = I*omega constant.

Static equilibrium condition

An object is in static equilibrium only if BOTH the net force is zero AND the net torque about any pivot is zero.

Unit 5: Momentum

Momentum

The product of an object's mass and velocity, p = mv; a vector quantity measured in kg·m/s.

Impulse

The change in momentum caused by a net force acting over a time interval: J = FΔt = Δp.

Conservation of Momentum

In an isolated system with no net external force, total momentum before an event equals total momentum after.

Elastic Collision

A collision in which both total momentum and total kinetic energy are conserved.

Inelastic Collision

A collision in which momentum is conserved but kinetic energy is not; some energy converts to heat, sound, or deformation.

Perfectly Inelastic Collision

A collision where the colliding objects stick together and move with a common final velocity: m1v1+m2v2=(m1+m2)$v_f$.

Impulse-Momentum Theorem

States that the impulse delivered to an object equals its change in momentum, connecting force-time behavior to velocity change.

Center of Mass

The mass-weighted average position of a system, which moves at constant velocity unless acted on by a net external force, unaffected by internal collisions or explosions.

Recoil

The backward momentum of an object (e.g., a gun) that results from conservation of momentum when it propels another object (e.g., a bullet) forward.

Force-Time Graph

A graph whose area under the curve equals the impulse delivered to an object during that time interval.

Unit 6: Energy & Work

Work

The energy transferred by a force acting through a displacement: W = Fd cosθ, measured in joules.

Work-Energy Theorem

The net work done on an object equals its change in kinetic energy: $W_{net}$ = ΔKE.

Kinetic Energy

The energy of motion, KE = ½mv²; proportional to mass and to the square of speed.

Gravitational Potential Energy

Stored energy due to height in a gravitational field, $U_g$ = mgh, measured relative to a chosen reference level.

Elastic Potential Energy

Energy stored in a stretched or compressed spring, $U_s$ = ½kx², where k is the spring constant and x the displacement from equilibrium.

Conservation of Mechanical Energy

In the absence of non-conservative forces, KE + PE remains constant throughout a system's motion.

Power

The rate of doing work or transferring energy, P = W/t = Fv cosθ, measured in watts (J/s).

Conservative Force

A force (like gravity or spring force) whose work done is path-independent, allowing a potential energy to be defined.

Hooke's Law

The restoring force of an ideal spring: F = −kx, proportional and opposite to the displacement from equilibrium.

Non-Conservative Force

A force like friction whose work depends on the path taken, converting mechanical energy into other forms such as heat.

Unit 7: Electrostatics & Circuits

Coulomb's Law

F = k*q1*q2/$r^2$, where k = 8.99x10^9 N*$m^2/C^2$; describes the electrostatic force between two point charges.

Electric field

E = F/q = k*Q/$r^2$ (from a point charge), the force per unit positive test charge; units N/C.

Electric potential

V = U/q, measured in volts (J/C); potential difference (voltage) drives current flow between two points.

Ohm's Law

V = IR, relating voltage, current, and resistance for ohmic materials.

Resistance of a wire

R = rho*L/A, increasing with length and resistivity, decreasing with cross-sectional area.

Electric power in a circuit

P = IV = $I^2$*R = $V^2/R$, the rate of electrical energy transfer or dissipation.

Series circuit rule

Resistors in series share the same current; $R_{eq} = R1 + R2$ + ...; voltage divides among them.

Parallel circuit rule

Resistors in parallel share the same voltage; 1/$R_{eq} = 1/R1 + 1/R2$ + ...; current divides among them.

Kirchhoff's Junction Rule

The total current entering a junction equals the total current leaving it (conservation of charge).

Kirchhoff's Loop Rule

The sum of voltage changes around any closed circuit loop equals zero (conservation of energy).

Unit 8: Magnetism

Force on a moving charge

F = qvB sinθ; maximum when v is perpendicular to B, zero when parallel to B.

Force on a current-carrying wire

F = BIL sinθ; direction given by the right-hand rule using the current direction.

Magnetic field of a straight wire

B = μ₀I/(2πr), μ₀ = 4π×10⁻⁷ T·m/A; field lines form circles around the wire.

Right-hand rule (force)

Point fingers along v, curl toward B; thumb gives F for a positive charge (reverse for negative).

Radius of circular motion in a field

r = mv/(qB), from setting the magnetic force equal to the centripetal force requirement.

Faraday's Law

Induced EMF = −N(ΔΦ/Δt); an EMF is induced only by a CHANGING magnetic flux.

Lenz's Law

The induced current flows in the direction that opposes the change in flux that produced it.

Generator vs. motor

A generator converts mechanical energy to electrical energy; a motor does the reverse.

Like vs. unlike magnetic poles

Like poles (N-N, S-S) repel; unlike poles (N-S) attract — magnetic poles always come in N-S pairs.

Parallel current-carrying wires

Wires with current in the same direction attract; opposite directions repel.

Unit 9: Waves & Sound

Wave equation

v = f*lambda, relating wave speed, frequency, and wavelength; frequency is set by the source and does not change across media.

Wave speed on a string

v = $sqrt{F_T/mu}$, where $F_T$ is string tension and mu is linear mass density (mass per length).

Constructive interference

Occurs when waves meet in phase (path difference = n*lambda), producing a larger combined amplitude.

Destructive interference

Occurs when waves meet out of phase (path difference = (n+1/2)*lambda), reducing or canceling amplitude.

Standing wave on a string fixed at both ends

Harmonic frequencies $f_n = n$*v/(2L) for n = 1, 2, 3,...; supports all integer harmonics.

Standing wave in a pipe closed at one end

Only odd harmonics exist: $f_n = n$*v/(4L) for n = 1, 3, 5,...

Doppler effect

The observed frequency shifts when source and observer move relative to each other: frequency rises on approach, falls on recession.

Beat frequency

$f_{beat}$ = |f1 - f2|, the periodic loudness variation heard when two waves of close but different frequencies interfere.

Speed of sound in air

Approximately 343 m/s at room temperature; sound is a longitudinal wave requiring a medium to travel.

Decibel scale for sound intensity

beta = 10*log10(I/I0), where I0 = $10^{-12}$ W/$m^2$ is the threshold of human hearing.

Unit 10: Optics

Law of reflection

Angle of incidence = angle of reflection, both measured from the normal.

Mirror/lens equation

1/dₒ + 1/dᵢ = 1/f, relating object distance, image distance, and focal length.

Magnification

m = −dᵢ/dₒ = hᵢ/hₒ; negative m means inverted, |m|>1 means magnified.

Snell's Law

n₁ sinθ₁ = n₂ sinθ₂, where n = c/v is the index of refraction of each medium.

Index of refraction

n = c/v; light bends toward the normal entering a higher-n (denser) medium.

Critical angle

sinθc = n₂/n₁ (going from higher n to lower n); beyond θc, total internal reflection occurs.

Concave mirror image types

Object beyond f: real, inverted image. Object inside f: virtual, upright, magnified image.

Convex mirror/diverging lens

Always produce a virtual, upright, reduced image, regardless of object distance.

Converging lens (object inside f)

Produces a virtual, upright, magnified image — the principle behind a magnifying glass.

Dispersion

Index of refraction depends slightly on wavelength, so a prism spreads white light into a spectrum (violet bends most, red least).

Unit 11: Modern Physics

Photon energy

E = hf = hc/λ, where h = 6.63×10⁻³⁴ J·s (Planck's constant).

Photoelectric effect (KEmax)

KEmax = hf − φ, where φ is the metal's work function; increasing intensity increases electron count, not KEmax.

De Broglie wavelength

λ = h/p = h/(mv); every moving particle has an associated wavelength.

Atomic energy levels

Electrons occupy discrete, quantized energy levels; transitions absorb/emit photons with E = |ΔE|.

Alpha decay

Emits a helium nucleus; mass number drops by 4, atomic number drops by 2.

Beta-minus decay

A neutron converts to a proton, emitting an electron; atomic number increases by 1, mass number unchanged.

Gamma decay

Emits a high-energy photon; neither mass number nor atomic number changes.

Half-life

N = N₀(1/2)^(t/T); the time for half of a radioactive sample to decay, independent of sample size.

Mass-energy equivalence

E = mc²; the mass defect in a nuclear reaction converts into released energy.

Fission vs. fusion

Fission splits a heavy nucleus into lighter ones; fusion combines light nuclei into a heavier one — both release energy.