AP Physics 1 · Unit 5 · Rotation

Torque and Moment of Inertia Practice Problems

See how the axis and mass distribution determine rotational inertia. Calculate the inertia of a rectangular package frame, infer a polishing wheel’s mass, size a fan motor, analyze tethered flight, and compare bicycle sprockets.

12 questions6 conceptual · 6 calculation

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Simulation scene from the Torque and Moment of Inertia lesson. — A scene from the related lesson. Open the practice to work through the questions.

What you’ll practice

Connect mass distribution to angular acceleration

Choose the correct axis and inertia

Use perpendicular distance for point masses. Combine a disk and radial rods, distinguish a hoop from a solid cylinder, and shift a rod’s axle with the parallel-axis theorem.

Account for every torque

Calculate tangential thrust and chain-drive torque. Keep motor torque, brake torque, and net torque separate before applying Στ = Iα.

Connect rotation to linear motion

Use angular acceleration to find final angular speed and tangential acceleration. Distinguish the inward acceleration of circular motion from the component that changes speed.

A question from this set

Move the masses outward

Two equal point masses are fixed to light spokes on opposite sides of an axle. Each distance from the axle is doubled while the same net torque is applied. How does their angular acceleration change?

It becomes one quarter as large.
It becomes half as large.
It doubles.

Try it in the practice set

Compare the same two masses at different distances from the axle while keeping net torque fixed.

Key ideas

The same torque can produce different angular accelerations

Distance from the axis enters as a square

A point mass contributes mr² using the shortest distance to the chosen axis. Moving masses outward can change rotational inertia much more than the same factor changes their distances.

Applied torque must overcome resistance

A motor accelerating a rotor against bearing resistance supplies more torque than Iα alone. At steady angular velocity, nonzero driving and resisting torques can balance.

See the physics

Compare the measured angular-velocity slopes

After attempting a question, run the native force-driven models and compare torque, rotational inertia, and the slope of angular velocity. Switch mass placements, disk and hoop shapes, bearing resistance, axes, or sprockets. The tethered drone uses a taut string and tangent-following thrust.

Use a hint for a starting point or open a worked solution to follow the reasoning. Your progress saves in this browser, so you can return to unfinished questions.

Ready for torque and moment of inertia?

Begin with a conceptual question, then work through the calculations.

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