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Volume I · MMXXVI AP Physics C: Mechanics
Library› AP Physics C: Mechanics› Unit 5: Torque and Rotational Dynamics
⁂   AP Physics C: Mechanics · Unit 5

5. Torque and Rotational Dynamics

10–15% of the AP exam. 8 key topics. 4 common errors analyzed.

10–15% exam weight

Unit 5: Torque and Rotational Dynamics

Unit 5 (Torque and Rotational Dynamics) is part of the calculus-based AP Physics C: Mechanics curriculum. Variable-force problems and differential equations require calculus setup; show your integral expression before evaluating.

Key topics in this unit

  1. Rotational kinematics: angular displacement, angular velocity, angular acceleration
  2. Kinematic relationships between linear and rotational quantities: v = rω, a_t = rα
  3. Torque: τ = r × F (magnitude τ = rF sinθ)
  4. Rotational inertia (moment of inertia): I = ∫r² dm
  5. Parallel-axis theorem: I = I_cm + Md²
  6. Rotational equilibrium: Στ = 0
  7. Newton's Second Law for rotation: τ_net = Iα
  8. Connecting translational and rotational Newton's Second Law for systems with both

Common errors — what the rubric penalizes

These are the most frequently penalized mistakes on AP exam FRQs and MCQs. Review each before your next practice session.

Common error

Using I = mr² (point-mass formula) for extended objects instead of the correct distributed-mass result; failing to apply the parallel-axis theorem when the rotation axis is not through the center of mass

Common error

Torque direction sign errors: not applying the right-hand rule consistently, or failing to account for which torques are clockwise vs. counterclockwise relative to the chosen pivot

Common error

Setting up moment of inertia integrals with incorrect mass elements — using dm = ρ dV but substituting an area or length element appropriate for a different geometry (e.g., using a ring element dm = ρ·2πr·dr for a disk problem with non-uniform density)

Common error

In combined translational-rotational Newton's Law problems (e.g., a mass on a string wrapped around a pulley), writing one equation for the whole system instead of separate F=ma and τ=Iα equations for each part, then linking them via the no-slip constraint a = rα

Study checklist

  • Can you list all key topics from memory without this page?
  • Have you worked through at least one FRQ-style question per topic?
  • Can you explain each common error above — and why the correct answer differs?
  • Have you reviewed the relevant College Board CED section and formula sheet entries?
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