AP Physics 1 Study Guide: Mechanics, Waves, and the Lab Questions Nobody Prepares For

AP Physics 1 is algebra-based, but "algebra-based" does not mean easier than AP Physics C. It means the mathematical barrier is lower — but the conceptual demands are just as high, and the exam specifically tests whether you can reason from physics principles rather than follow a formula. Students who approach it as a calculation course typically score 2 or 3; students who approach it as a conceptual reasoning course with calculations score 4 or 5.

The most useful preparation mindset: for every equation you learn, ask "what does this mean physically?" before asking "how do I use this formula?"

Kinematics: motion without forces

One-dimensional motion: The five kinematics equations apply to constant acceleration:

• v = v₀ + at
• x = x₀ + v₀t + ½at²
• v² = v₀² + 2a(x − x₀)
• x = x₀ + ½(v₀ + v)t

Know when each applies (all require constant acceleration). Know the sign convention: pick positive direction first, then assign signs consistently. Velocity and acceleration can have opposite signs (deceleration).

Graphical kinematics: From position-time graph: slope = velocity. From velocity-time graph: slope = acceleration, area under curve = displacement. From acceleration-time graph: area = change in velocity. Graph interpretation is tested heavily in multiple choice.

Projectile motion: Horizontal: constant velocity (aₓ = 0), x = v₀ₓt. Vertical: constant acceleration g downward, same equations as 1D. Key insight: horizontal and vertical motions are independent. Time of flight is determined by vertical motion alone.

Dynamics: Newton's laws and free body diagrams

Newton's Second Law: ΣF = ma. "Net force" means vector sum of all forces. Always draw a free body diagram before writing equations. For each object in the system, each force on it appears as an arrow from the object's centre.

Common force types: Gravity (W = mg, downward), Normal force (perpendicular to surface, away from surface), Tension (along rope, away from object), Friction (static: up to μₛN; kinetic: exactly μₖN, opposing relative motion), Spring force (Hooke's Law: F = −kx toward equilibrium).

Circular motion: The net force toward the centre of the circle provides centripetal acceleration: ΣF_centripetal = mv²/r. The centripetal force is not a new type of force — it is the net inward force provided by tension, gravity, normal force, or some combination. Common error: students draw "centripetal force" as a separate arrow on the free body diagram — this is wrong.

Newton's Third Law pairs: For every force A exerts on B, B exerts an equal and opposite force on A. The two forces act on different objects. This is tested through ranking problems and systems of objects.

Energy and momentum: conservation laws

Work-energy theorem: Net work = change in kinetic energy. Work = Fd cos θ (F and d parallel) or more precisely W = F · d for one-dimensional work. Potential energy: gravitational Uₘ = mgh; spring Uₛ = ½kx². Conservation of energy: E_total = KE + PE + thermal energy; total is constant when no external non-conservative forces act.

Collisions: In all collisions, momentum is conserved (if net external force = 0). Elastic collisions: both momentum and KE conserved. Perfectly inelastic collisions: objects stick together, maximum KE lost. Inelastic: momentum conserved but KE not. Calculate final velocities using conservation equations: m₁v₁ᵢ + m₂v₂ᵢ = m₁v₁f + m₂v₂f.

Impulse-momentum theorem: J = ΔP = FΔt. Area under force-time graph equals impulse (change in momentum). Used for impact problems.

Rotational dynamics

Torque: τ = rF sinθ where r is the distance from the pivot and θ is the angle between r and F. Maximum torque when force is perpendicular to the moment arm (θ = 90°).

Rotational inertia: I depends on mass distribution — I = Σmr². Greater I means harder to angularly accelerate. Key values: point mass (mr²), solid disk (½mr²), hoop (mr²), solid sphere (⅖mr²). Rotational version of Newton's Second Law: τ_net = Iα.

Angular momentum conservation: L = Iω is conserved when net torque = 0. Classic example: a spinning figure skater pulling arms in reduces I, so ω increases to keep L = Iω constant. An AP favourite.

Rolling without slipping: v = rω. Both translational and rotational KE contribute: E_total = ½mv² + ½Iω².

Simple harmonic motion

Spring-mass: Period T = 2π√(m/k). Does not depend on amplitude. Frequency f = 1/T. At equilibrium: all energy is kinetic, maximum speed. At maximum displacement: all energy is potential, momentarily at rest.

Pendulum: Period T = 2π√(L/g). Depends on L and g only — not on mass or amplitude (for small angles). This is tested by asking what happens to period if mass doubles (no change) or if moved to a higher-gravity planet (decreases).

Waves and circuits

Mechanical waves: v = fλ. Standing waves on a string fixed at both ends: L = n(λ/2), so λ_n = 2L/n and f_n = nv/(2L). Nodes at the fixed ends.

Circuits: Ohm's law: V = IR. Series: same current through all; V_total = ΣV; R_total = ΣR. Parallel: same voltage; I_total = ΣI; 1/R_total = Σ(1/R). Power: P = IV = I²R = V²/R.

Experimental design questions

These free-response questions ask you to design an experiment to test a physics principle. Always specify: independent variable (what you vary), dependent variable (what you measure), control variables (what you hold constant), procedure (with enough detail for replication), data analysis method (how the data answers the question). State what graph you would plot and how its slope or intercept would confirm the physics relationship.

Use the Pomodoro Timer for timed free-response practice. The AP Calculus AB study guide covers the calculus that underpins AP Physics C: Mechanics if you plan to continue to that course.