AP Physics C: Mechanics ›  Unit 5

Unit 5 Torque and Rotational Dynamics

Everything from Unit 2 — but now it spins. Torque replaces force, rotational inertia replaces mass, and the same free-body diagrams get a new job.

📋 10–15% AP Exam Weighting🕐 ~14–20 Class Periods📺 6 Episodes✅ Progress Check 5
EP.5.1

Rotational Kinematics

Angular displacement, velocity, and acceleration — the same three-quantity structure as Unit 1, just measured in radians instead of meters.

Δθ = θ − θ₀Angular velocity ωAngular acceleration α
🕐 2–3 class daysOpen lesson →
EP.5.2

Connecting Linear and Rotational Motion

Every point on a spinning rigid body has a linear velocity and acceleration — they just depend on how far that point sits from the axis.

v = rωa_t = rαRolling motion
🕐 2–3 class daysOpen lesson →
EP.5.3

Torque

Force alone doesn't tell you if something will spin — you need where it's applied, too. Torque is a cross product, and the right-hand rule tells you which way things turn.

τ = r × F|τ| = rF sinθRight-hand rule
🕐 3–4 class daysOpen lesson →
EP.5.4

Rotational Inertia

Mass resists acceleration; rotational inertia resists angular acceleration. Where the mass sits relative to the axis matters as much as how much of it there is.

I = Σmᵢrᵢ²I = ∫r² dmMass distribution matters
🕐 2–3 class daysOpen lesson →
EP.5.5

Rotational Equilibrium and Newton's First Law in Rotational Form

A system can spin at constant angular velocity while accelerating translationally, or vice versa — the two equilibriums don't have to travel together.

Στ = 0Rotational equilibriumIndependent of ΣF = 0
🕐 2–3 class daysOpen lesson →
EP.5.6

Newton's Second Law in Rotational Form

τ_net = Iα is F = ma's rotational twin. Same logic, same structure — inertia just means something different when things spin.

τ_net = Iαα = τ_net/IDirect rotational analog of F = ma
🕐 3–4 class daysOpen lesson →
🎓 AP Classroom — Progress Check 5
~18 multiple-choice · 4 free-response · Covers all 6 episodes
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