AP Physics 1 · Unit 5 · Rotation

Torque with Newton’s Laws Practice Problems

Connect force equations for translating objects to torque equations for rotating ones. Compare unequal tensions in an Atwood machine, a falling rod’s initial accelerations, a rope-driven disk, a cart and hanging load, and a spool unwinding from a fixed string.

12 questions6 conceptual · 6 calculation

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Simulation scene from the Torque with Newton’s Laws lesson. — A scene from the related lesson. Open the practice to work through the questions.

What you’ll practice

Use separate equations linked by one motion constraint

Choose each body and its axis

Write Newton’s second law for each moving mass, then take moments about the pulley axle or rod pin. Forces through the chosen axis can have zero torque while still appearing in force equations.

Connect translation and rotation

Apply a = Rα and v = Rω only when the cord does not slip. Compare the tangential accelerations of a rod’s center and end without assuming they equal g.

Solve tensions and design parameters

Include pulley inertia in the acceleration denominator, calculate each side’s tension, and find a pulley mass that produces a target acceleration.

A question from this set

Two tensions around a massive pulley

An Atwood machine has a lighter mass on the left and a heavier mass on the right. A light cord turns a massive pulley without slipping, and the heavier mass accelerates down. How do the two cord tensions compare?

The right-side tension is larger, supplying the pulley’s clockwise net torque.
They must be equal because the cord is light.
The left-side tension is larger because the left mass accelerates upward.

Try it in the practice set

Identify the two hanging masses and the massive pulley. Compare the tensions acting on each mass with the torque they supply about O.

Key ideas

One light cord can have two different tensions

A massive pulley needs a torque difference

For an accelerating pulley with equal rim radii, the difference between the two tensions supplies its net torque. Equal tensions are the negligible-inertia limit, not a universal property of a light cord.

A fixed support does not mean equilibrium

A spool can accelerate downward while unwinding from a string fixed at its upper end. Its weight and tension determine translation, while the off-center tension determines rotation about its center.

See the physics

Measure connected motion under actual cord constraints

After attempting the questions, inspect the measured side tensions, linear acceleration, pulley rotation, and no-slip travel graphs. Compare pulley radii and inertia, watch a rod fall under its own weight, and record a spool crossing its descent marker.

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 with newton’s laws?

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

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