AP Physics 1 · Unit 6 · Rotating Systems

Rotational Kinetic Energy Practice Problems

Separate the energy of a moving center from the energy of spin. Compare rolling hoops, cylinders, spheres and shells, calculate work from a string pull or constant torque, and track energy shared by a falling bucket and a fixed spool.

12 questions6 conceptual · 6 calculation

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Simulation scene from the Rotational Kinetic Energy lesson. — A scene from the related lesson. Open the practice to work through the questions.

What you’ll practice

Account for translation, rotation, gravity, and work

Choose each kinetic-energy term

Use ½Mv² for center-of-mass motion and ½ICMω² for spin about the center. Keep fixed-axis rotation separate from rolling translation so energy is not counted twice.

Compare shapes at the same vertical drop

Use the correct hoop, cylinder, sphere and shell inertias. Explain why the fastest center has the smallest rotational share when equal masses roll from the same height.

Calculate rotational work and final speed

Use Fs for a string pull and τΔθ for a constant torque. Convert revolutions to radians and include both the bucket’s translation and the fixed spool’s rotation.

A question from this set

Angular speed and rotation direction

A rotor has fixed moment of inertia I. If its angular speed doubles, how does its rotational kinetic energy change?

It becomes four times as large.
It becomes twice as large.
It becomes negative if the rotation is clockwise.

Try it in the practice set

Keep inertia fixed while comparing baseline angular speed, twice that speed, and reversed rotation.

Key ideas

Equal total energy can have different translational and rotational shares

The inertia coefficient controls the split

For I = kMR² and rolling without slipping, total kinetic energy is ½Mv²(1 + k). At a shared vertical drop, a larger rotational share means a smaller center speed.

Energy does not inherit the sign of spin

Rotational kinetic energy depends on ω². Clockwise and counterclockwise rotation at the same speed have the same energy, while work depends on torque and angular displacement together.

See the physics

Watch measured energy contributions exchange and add

After attempting the questions, compare recorded translational, rotational and gravitational energies with initial energy plus supplied work. Switch shapes or peg radii, reverse a torque-driven rotor, and measure the bucket and sphere at their actual markers.

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 rotational kinetic energy?

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

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