AP Physics 1: Algebra-Based, AP exams, 5–8%

Unit 6: Energy and Momentum of Rotating Systems

Unit 6 extends energy and momentum conservation into rotation. Rotational kinetic energy, angular momentum, and angular impulse are defined, then applied to rolling motion and orbiting satellites. Problems that combine translation and rotation, such as a rolling object on a ramp, are the characteristic form.

Position: 6 of 8 units
Published weighting: 5–8% in the official framework
Topics covered: 5 topics in this guide

What is covered

Topics inside this unit.

These topics describe the scope students most often review for this part of AP Physics 1: Algebra-Based. Treat them as a study checklist rather than an exhaustive list of what a single exam form can sample.

Rotational kinetic energy: Energy stored in rotation, and combining it with translational kinetic energy for rolling objects.
Torque and work: Work done by a torque through an angular displacement, and rotational power.
Angular momentum and angular impulse: Angular momentum for point masses and rigid bodies, and the change produced by a torque over time.
Conservation of angular momentum: When angular momentum is conserved, and why changing rotational inertia changes angular speed.
Rolling and orbital motion: Rolling without slipping, and applying energy and angular momentum conservation to satellite orbits.

Study tips

How to practice Rotating Systems.

Section-specific guidance that follows from how this material is usually tested.

Practice rolling problems as combined energy accounts: translational plus rotational, sharing one constraint.
Explain the spinning-skater example in terms of rotational inertia rather than intuition.
Check whether external torques act before invoking conservation of angular momentum.

Where this fits

Unit 6: Energy and Momentum of Rotating Systems is 6 of 8 units in the AP Physics 1: Algebra-Based guide, and it carries a published weighting of 5–8% in the official framework. Use the full guide to balance it against everything else you have to review.

Back to the AP Physics 1: Algebra-Based guide Official exam information

Sample Rotating Systems questions

Practice questions, not yet expert-reviewed

Original practice questions written to the published framework for this section. No expert has reviewed them, and they are not taken from any official exam. Try each one before you open the answer.

Question 1Foundational
A flywheel with rotational inertia 4.0 kg m^2 spins about its axle at an angular speed of 3.0 rad/s. What is its rotational kinetic energy?
1. A6.0 J
2. B12 J
3. C18 J
4. D36 J
Show answer
Answer: C. 18 J
Rotational kinetic energy is (1/2)I(omega)^2 = (1/2)(4.0)(3.0)^2 = 18 J. The 36 J choice omits the factor of one half, and 12 J is the angular momentum I times omega rather than an energy.
Key insight: Rotational kinetic energy has the same form as (1/2)mv^2 with rotational inertia replacing mass and angular speed replacing speed.
Question 2Foundational
A 2.0 kg point mass travels in a circle of radius 3.0 m at a constant speed of 4.0 m/s. What is the magnitude of its angular momentum about the center of the circle?
1. A8.0 kg m^2/s
2. B12 kg m^2/s
3. C24 kg m^2/s
4. D72 kg m^2/s
Show answer
Answer: C. 24 kg m^2/s
For a point mass moving perpendicular to the radius, L = mvr = (2.0 kg)(4.0 m/s)(3.0 m) = 24 kg m^2/s. The 8.0 kg m^2/s choice leaves out the radius, which is what distinguishes angular momentum from linear momentum.
Key insight: Angular momentum always references a specific axis, because it depends on the distance from that axis.
Question 3Intermediate
A skater spinning on frictionless ice at 2.0 rad/s pulls her arms inward, reducing her rotational inertia from 6.0 kg m^2 to 2.0 kg m^2. What is her new angular speed?
1. A0.67 rad/s
2. B2.0 rad/s
3. C6.0 rad/s
4. D12 rad/s
Show answer
Answer: C. 6.0 rad/s
No external torque acts, so angular momentum is conserved: (6.0)(2.0) = (2.0)(omega) gives omega = 6.0 rad/s. The 0.67 rad/s choice inverts the ratio, which would mean pulling the arms in slows the skater down.
Key insight: Reducing rotational inertia with no external torque speeds up the spin and increases kinetic energy, with the extra energy supplied by the skater's muscles.
Question 4Intermediate
A uniform solid disk and a hoop have the same mass and the same radius. Both are released from rest at the same height on a ramp and roll without slipping to the bottom. Which one reaches the bottom first?
1. AThe disk
2. BThe hoop
3. CThey reach the bottom at the same time
4. DIt depends on the angle of the ramp
Show answer
Answer: A. The disk
The hoop has all of its mass at the rim, so its rotational inertia MR^2 is larger than the disk's (1/2)MR^2 and a greater share of the released potential energy goes into rotation rather than translation. The disk therefore has the larger acceleration and arrives first, regardless of mass or radius.
Key insight: In a rolling race only the shape matters: the object with mass closer to its axis always wins.
Question 5Advanced
A disk with rotational inertia 2.0 kg m^2 spins freely at 6.0 rad/s about a vertical axle. A second, non-rotating disk with rotational inertia 4.0 kg m^2 is dropped onto it, and the two then rotate together about the same axle. How much kinetic energy is lost in the process?
1. A0 J
2. B12 J
3. C24 J
4. D36 J
Show answer
Answer: C. 24 J
Angular momentum is conserved, so (2.0)(6.0) = (6.0)(omega) gives a common angular speed of 2.0 rad/s. The kinetic energy falls from (1/2)(2.0)(6.0)^2 = 36 J to (1/2)(6.0)(2.0)^2 = 12 J, a loss of 24 J to friction between the surfaces.
Key insight: Conserved angular momentum does not mean conserved energy: this rotational collision is inelastic just like its linear counterpart.

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Unit 6: Energy and Momentum of Rotating Systems