AP Physics 1 cheat sheet

Average velocity is displacement over elapsed time: v_avg = Δx/Δt; average speed uses total distance instead.

For constant acceleration: v = v₀ + at, Δx = v₀t + ½at², v² = v₀² + 2aΔx.

Displacement is a vector; on a velocity-time graph it equals the signed area between the curve and the time axis.

Instantaneous acceleration is the slope of the velocity-time graph; instantaneous velocity is the slope of the position-time graph.

Free fall near Earth's surface uses a = g ≈ 9.8 m/s² downward, independent of mass when air resistance is negligible.

Projectile motion separates into independent axes: constant horizontal velocity and vertical acceleration g.

At the top of a projectile's path the vertical velocity component is zero but the horizontal component is unchanged.

Relative velocity adds as vectors: v_A/C = v_A/B + v_B/C.

Newton's second law: ΣF = ma, with forces summed as vectors in a chosen coordinate system.

Newton's first law: net force zero means velocity is constant, which includes remaining at rest.

Newton's third law pairs act on different objects, so they never cancel in a single free-body diagram.

Static friction satisfies f_s ≤ μ_sN; kinetic friction is f_k = μ_kN and opposes relative sliding.

On an incline, the component of weight along the slope is mg sin θ and the normal force is mg cos θ.

For a mass on a string in a vertical circle, the net inward force at the top is T + mg.

Centripetal acceleration has magnitude v²/r directed toward the center; it is not a separate force.

Drag increases with speed and produces terminal velocity where drag equals weight, giving zero acceleration.

Work by a constant force is W = Fd cos θ, where θ is the angle between force and displacement.

Work-kinetic energy theorem: W_net = ΔK = ½mv² − ½mv₀².

Gravitational potential energy near Earth is U = mgh; spring potential energy is U = ½kx².

For a conservative force, W = −ΔU and mechanical energy is conserved when only conservative forces do work.

Nonconservative work changes mechanical energy: W_nc = ΔK + ΔU.

Power is the rate of energy transfer: P_avg = W/Δt and P = Fv cos θ for constant force.

A force perpendicular to displacement (such as centripetal force) does zero work and changes no kinetic energy.

Spring force F = −kx obeys Hooke's law for an ideal spring within its elastic limit.

Momentum is p = mv, a vector pointing along the velocity.

Impulse equals change in momentum: J = F_avgΔt = Δp; the area under a force-time graph is impulse.

Total momentum is conserved when the net external force on the system is zero, even during collisions.

Elastic collisions conserve kinetic energy; perfectly inelastic collisions stick together and lose the most kinetic energy.

In a perfectly inelastic collision, v_f = (m₁v₁ + m₂v₂)/(m₁ + m₂).

The center of mass moves as if all external forces acted there: F_net = Ma_cm.

Explosions and recoil conserve momentum starting from zero total momentum, giving equal and opposite momenta.

Kinetic energy is conserved only in elastic collisions, so momentum conservation alone does not determine energy outcomes.

Torque is τ = rF sin θ, with θ measured between the position vector and the force; direction follows the right-hand rule.

Rotational equilibrium requires net torque zero about any chosen pivot point.

Moment of inertia I = Σmr² depends on mass distribution and on the axis chosen.

Rotational form of Newton's second law: Στ = Iα.

For a hoop I = MR² about its center; for a solid disk I = ½MR²; for a solid sphere I = (2/5)MR².

Parallel-axis theorem: I = I_cm + Md², where d is the distance from the center of mass to the new axis.

Angular kinematics mirror linear kinematics: ω = ω₀ + αt, Δθ = ω₀t + ½αt², ω² = ω₀² + 2αΔθ.

Rolling without slipping links motion by v = ωR and a = αR.

Rotational kinetic energy is K = ½Iω²; a rolling object's total K adds ½mv² for its center of mass.

Angular momentum is L = Iω for a rigid body and L = rmv sin θ for a point mass about a pivot.

Angular momentum is conserved when net external torque is zero, as when a skater pulls in her arms to spin faster.

Work done by torque is W = τΔθ; rotational power is P = τω.

Rolling objects released from the same height arrive together only if their I/(MR²) ratios match.

A rolling object's speed at the bottom of a ramp follows v² = 2gh/(1 + I/(MR²)).

A collision that sticks an object to a rotating system conserves angular momentum but generally not kinetic energy.

Rotational impulse is τΔt = ΔL, the angular analog of force impulse changing linear momentum.

Simple harmonic motion requires a restoring force proportional to displacement: F = −kx.

For a mass-spring system, ω = √(k/m) and T = 2π√(m/k), independent of amplitude.

For a simple pendulum, T = 2π√(L/g) for small angles, independent of mass and amplitude.

Position follows x = A cos(ωt + φ); velocity leads displacement by 90° and acceleration is opposite displacement.

Maximum speed is v_max = Aω, occurring at equilibrium where acceleration is zero.

Maximum acceleration is a_max = Aω², occurring at maximum displacement where speed is zero.

Total mechanical energy of a spring oscillator is E = ½kA², constant when damping is negligible.

Resonance occurs when driving frequency matches the natural frequency, producing maximum amplitude.

Density is ρ = m/V; pressure is P = F/A measured in pascals.

Gauge pressure at depth h in a fluid at rest is P = ρgh, added to any surface pressure.

Pascal's principle: pressure applied to an enclosed fluid transmits undiminished, enabling hydraulic lift force multiplication.

Buoyant force equals the weight of displaced fluid: F_b = ρ_fluid V_displaced g.

An object floats when its average density is less than the fluid's; it displaces fluid whose weight equals its own weight.

Continuity equation for incompressible flow: A₁v₁ = A₂v₂, so narrower pipes carry faster flow.

Bernoulli's equation: P + ½ρv² + ρgy is constant along a streamline for ideal, nonviscous flow.

Where fluid speed increases, pressure decreases, which explains lift and the behavior of a Venturi tube.