Everything you need to master Unit 5 — angular motion, torque, rotational inertia, equilibrium, and Newton's laws in rotational form. The rotational version of everything you learned in Units 1, 2, and 4.
10–15% of the AP exam
7 study resources
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Seven free resources for Unit 5 — pick the one that fits how you learn.
Unit 5 takes the linear physics you've learned (position, velocity, acceleration, force, Newton's laws) and translates ALL of it into rotational terms. The good news: there's a perfect one-to-one analogy. Every linear quantity has a rotational counterpart. Master that table of analogies, and most of Unit 5 is review.
The College Board breaks Unit 5 into 6 topics: (5.1) Rotational Kinematics, (5.2) Connecting Linear and Rotational Motion, (5.3) Torque, (5.4) Rotational Inertia, (5.5) Rotational Equilibrium and Newton's First Law in Rotational Form, and (5.6) Newton's Second Law in Rotational Form. The key new concepts are torque (the rotational analog of force) and rotational inertia (the rotational analog of mass).
Unit 5 makes up about 10–15% of the AP exam. Even better — equilibrium problems (a uniform beam balanced on a pivot with weights hanging from it) show up almost every year, and they all follow the same recipe.
Key terms preview
A taste of what you'll find in The Essentials and Flashcards.
Angular Velocity (ω)
How fast something is rotating. ω = Δθ/Δt. Units: rad/s. The rotational analog of velocity.
Torque (τ)
τ = rF·sin(θ). The "rotational force" — what makes things spin faster or slower. Bigger lever arm = bigger torque.
Rotational Inertia (I)
An object's resistance to changes in rotation. Depends on mass AND how it's distributed about the axis. Bigger I = harder to spin up.
Newton's 2nd Law (Rotational)
τ_net = Iα. Net torque equals rotational inertia times angular acceleration. The rotational analog of F = ma.
Rotational Equilibrium
Στ = 0. No net torque means the object's angular velocity stays constant (could be zero, could be spinning).
Moment Arm (Lever Arm)
The perpendicular distance from the axis to the line of force. Longer lever arm = more torque for the same force.
1. Rotation has a perfect parallel to linear motion
Every linear quantity has a rotational analog: position ↔ angle, velocity ↔ angular velocity, acceleration ↔ angular acceleration, force ↔ torque, mass ↔ rotational inertia. All the kinematic equations and Newton's laws translate directly. Learn the analogy table and most of Unit 5 follows automatically.
2. Torque depends on force, distance, AND angle
τ = rF·sin(θ). To produce a torque, you need a force, AND a lever arm (distance from pivot), AND a component of force perpendicular to that lever arm. A force directly toward the pivot produces zero torque, no matter how big the force is. That's why doors have handles far from the hinges.
3. Rotational inertia depends on how mass is distributed
Two objects of equal mass can have very different rotational inertias depending on where the mass is located. Mass close to the axis spins easily; mass far from the axis is hard to spin up. That's why a long pole helps a tightrope walker stay balanced — its large rotational inertia resists rotation.