AP Physics 1 / Topic
Torque and Rotational Dynamics
Unit 5 extends Newton's laws to rotation: torque, rotational equilibrium (beams, seesaws, ladders), rotational inertia, angular kinematics, and Newton's second law for rotation.
What the exam asks
- Compute torque including the angle and lever-arm dependence
- Solve static equilibrium problems where net force and net torque are both zero
- Compare rotational inertias from mass distribution (point masses, rods, disks, hoops)
- Apply angular kinematics for constant angular acceleration
- Use Στ = Iα, including pulleys with mass and Atwood-style machines
Key formulas and rules
τ = rF sinθ (r from pivot to where the force acts)
ΣF = 0 and Στ = 0 about ANY pivot point
I = Σmr²; mass farther from axis ⇒ larger I
Στ = Iα
ω = ω0 + αt; θ = ω0t + ½αt²; linear links: v = rω, a = rα
Question bank breakdown
39
3
11 easy · 22 medium · 6 hard
Skills covered
Every question in the bank comes with a per-choice explanation, so you learn why each wrong answer is wrong — not just the key.
Sample question
From the free tier of the ScoreMint AP Physics 1 bank — try it, then check the answer.
A wheel starts from rest and accelerates uniformly at $4.0 \text{ rad/s}^2$ for $5.0 \text{ s}$. How many complete revolutions does the wheel make during this time?
- A. $4.0$ revolutions
- B. $7.9$ revolutions
- C. $10$ revolutions
- D. $15.9$ revolutions
Show answer and explanation
Answer: B. This problem applies rotational kinematics, which parallels linear kinematics. Starting from rest ($\omega_0 = 0$), the angular displacement is $\theta = \frac{1}{2}\alpha t^2 = \frac{1}{2}(4.0)(5.0)^2 = 50$ rad. To convert radians to revolutions, divide by $2\pi$: $50/(2\pi) \approx 7.96$ revolutions. The rotational kinematic equations have the same form as their linear counterparts: $\theta \leftrightarrow x$, $\omega \leftrightarrow v$, $\alpha \leftrightarrow a$.
Study tip
In beam problems, put the pivot at the point where an unknown force acts — that force's torque vanishes and the equation solves itself with one unknown.