• 56 questions

AP Physics C Rotational Motion Practice Test

Unofficial practice on torque, rotational inertia, angular momentum and rolling, following Units 5 and 6 of AP Physics C: Mechanics.

A wheel starts from rest and turns with a constant angular acceleration of 4 rad/s². What is its angular velocity after 3 s?

Pick an answer, then press Check answer. Then you see Correct or Not quite, with the reason. Keys: A to D pick, Enter checks.

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Unofficial practice questions, not affiliated with the College Board. Bank checked October 10, 2026.

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All 56 questions

Topic 5.1: Rotational kinematics 5

  • A disk spinning at 20 rad/s slows at a constant rate and stops in 5 s. Through what angle does it turn while stopping? Wikipedia, "Rotation around a fixed axis"; course topic 5.1
  • A turntable starts from rest with a constant angular acceleration of 4 rad/s². Through what angle does it turn in the first 3 s? Wikipedia, "Rotation around a fixed axis"; course topic 5.1
  • A wheel starts from rest and turns with a constant angular acceleration of 4 rad/s². What is its angular velocity after 3 s? Wikipedia, "Rotation around a fixed axis"; course topic 5.1
  • The angular position of a rotor is θ(t) = 2t³ − 3t, with θ in radians and t in seconds. What is its angular velocity at t = 2 s? Wikipedia, "Angular velocity"; course topic 5.1
  • On a graph of angular velocity against time, what does the area between the curve and the time axis give? Wikipedia, "Rotation around a fixed axis"; course topic 5.1
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Topic 5.2: Connecting linear and rotational motion 4

  • A flywheel has an angular acceleration of 3.0 rad/s². What is the tangential acceleration of a point 0.20 m from its axis? Wikipedia, "Rotation around a fixed axis"; course topic 5.2
  • A point on a rotating wheel is 0.50 m from the axis. The wheel turns at 6.0 rad/s. What is the linear speed of the point? Wikipedia, "Rotation around a fixed axis"; course topic 5.2
  • A wheel of radius 0.30 m turns through 10 rad. How far does a point on its rim travel along its circular path? Wikipedia, "Rotation around a fixed axis"; course topic 5.2
  • Two beads are glued to a rigid spinning disk, one at distance r from the axis and one at 2r. How do their motions compare? Wikipedia, "Rotation around a fixed axis"; course topic 5.2

Topic 5.3: Torque 5

  • A 20 N force acts on a wrench 0.50 m from the bolt, at an angle of 30° to the handle. What is the magnitude of the torque about the bolt? Wikipedia, "Torque"; course topic 5.3
  • A 20 N force is applied at right angles to a wrench, 0.40 m from the bolt. What torque does it exert about the bolt? Wikipedia, "Torque"; course topic 5.3
  • A force is applied to a door along a line that passes straight through the hinge. What torque does it exert about the hinge? Wikipedia, "Torque"; course topic 5.3
  • A position vector r points along +x and a force F points along +y. By the right-hand rule, in which direction does the torque r × F point? Wikipedia, "Torque"; course topic 5.3
  • What is the lever arm of a force about an axis? Wikipedia, "Torque"; course topic 5.3

Topic 5.4: Rotational inertia 6

  • A hoop and a solid disk have the same mass and the same radius. Each turns about the axis through its center. Which has the greater rotational inertia? Wikipedia, "Moment of inertia" and Wikipedia, "List of moments of inertia"; course topic 5.4
  • A uniform thin rod of mass M and length L has rotational inertia ML²/12 about its center. What does the parallel axis theorem give for an axis through one end? Wikipedia, "Parallel axis theorem" and Wikipedia, "List of moments of inertia"; course topic 5.4
  • A uniform thin rod of mass M and length L lies along the x-axis from x = 0 to x = L. Which integral gives its rotational inertia about a perpendicular axis through x = 0? Wikipedia, "List of moments of inertia"; course topic 5.4
  • Among all axes parallel to a given direction, which one gives a rigid body its smallest rotational inertia? Wikipedia, "Parallel axis theorem"; course topic 5.4
  • The rod with a 2.0 kg point mass at each end, 1.0 m apart, is now turned about a perpendicular axis through one of the masses. What is its rotational inertia? Wikipedia, "Moment of inertia"; course topic 5.4
  • Two 2.0 kg point masses sit at the ends of a light rod 1.0 m long. What is the rotational inertia about an axis through the center of the rod and perpendicular to it? Wikipedia, "Moment of inertia"; course topic 5.4

Topic 5.5: Rotational equilibrium 4

  • A 30 kg child sits 2.0 m from the pivot of a seesaw. How far from the pivot, on the other side, must a 40 kg child sit to balance it? Wikipedia, "Torque"; course topic 5.5
  • A fan blade assembly turns at a constant angular velocity. What must be true of the torques on it? Wikipedia, "Mechanical equilibrium"; course topic 5.5
  • A uniform beam 4.0 m long weighs 200 N and rests on a support at each end. A 600 N crate sits 1.0 m from the left end. What upward force does the right support exert? Wikipedia, "Torque"; course topic 5.5
  • Two forces of equal size and opposite direction act along the rim of a disk at opposite ends of a diameter, both urging it to turn the same way. The disk is free in space. What happens? Wikipedia, "Torque"; course topic 5.5

Topic 5.6: Newton's second law in rotational form 5

  • A 2.0 kg block hangs from a string wound on a solid disk pulley of mass 4.0 kg that turns freely. The block is released. Taking g = 10 m/s², what is the block's acceleration? Wikipedia, "List of moments of inertia" and Wikipedia, "Moment of inertia"; course topic 5.6
  • A net torque of 12 N·m acts on a flywheel whose rotational inertia is 3.0 kg·m². What is its angular acceleration? Wikipedia, "Moment of inertia"; course topic 5.6
  • A pulley is a solid disk of mass 4.0 kg and radius 0.50 m on a frictionless axle. A string wrapped around its rim is pulled with a steady 10 N. What is the pulley's angular acceleration? Wikipedia, "List of moments of inertia" and Wikipedia, "Moment of inertia"; course topic 5.6
  • In a lab, students apply several known net torques to a flywheel and plot its angular acceleration against net torque. The points lie on a straight line through the origin. What does the slope of the line equal? Wikipedia, "Moment of inertia"; course topic 5.6
  • The same net torque acts on two wheels. Wheel B has twice the rotational inertia of wheel A. How do their angular accelerations compare? Wikipedia, "Moment of inertia"; course topic 5.6

Topic 6.1: Rotational kinetic energy 4

  • A grinding wheel spins on a fixed axle, so its center of mass is at rest. Does the wheel have kinetic energy? Wikipedia, "Rotational energy"; course topic 6.1
  • A uniform rod 0.30 m long is pivoted at one end and released from rest in a horizontal position. Taking g = 10 m/s², what is its angular speed as it swings through the vertical? Wikipedia, "List of moments of inertia" and Wikipedia, "Rotational energy"; course topic 6.1
  • A wheel with rotational inertia 2.0 kg·m² spins at 3.0 rad/s. What is its rotational kinetic energy? Wikipedia, "Rotational energy"; course topic 6.1
  • The angular speed of a flywheel is doubled. By what factor does its rotational kinetic energy change? Wikipedia, "Rotational energy"; course topic 6.1

Topic 6.2: Torque and work 3

  • A constant torque of 5.0 N·m turns a shaft through 4.0 rad. How much work does the torque do? Wikipedia, "Torque"; course topic 6.2
  • A flywheel with rotational inertia 3.0 kg·m² starts from rest. A constant net torque of 6.0 N·m turns it through 4.0 rad. What is its final angular speed? Wikipedia, "Torque" and Wikipedia, "Rotational energy"; course topic 6.2
  • A graph shows the torque on a wheel as a function of its angular position. What does the area under the curve give? Wikipedia, "Torque"; course topic 6.2

Topic 6.3: Angular momentum and angular impulse 5

  • A 2.0 kg puck slides at 3.0 m/s along a straight line. The closest the line comes to point O is 4.0 m. What is the puck's angular momentum about O? Wikipedia, "Angular momentum"; course topic 6.3
  • A ball moves in a straight line that passes directly through point P. What is its angular momentum about P? Wikipedia, "Angular momentum"; course topic 6.3
  • A disk with rotational inertia 0.50 kg·m² spins at 8.0 rad/s. What is its angular momentum? Wikipedia, "Angular momentum"; course topic 6.3
  • A wheel has an angular momentum of 5.0 kg·m²/s. A net torque of 3.0 N·m then acts on it for 4.0 s in the direction of its spin. What is its angular momentum afterward? Wikipedia, "Angular momentum"; course topic 6.3
  • The angular momentum of a rotor is L(t) = 3t² + 2, in kg·m²/s with t in seconds. What is the net torque on it at t = 2 s? Wikipedia, "Angular momentum"; course topic 6.3

Topic 6.4: Conservation of angular momentum 6

  • A disk with rotational inertia 2.0 kg·m² spins at 6.0 rad/s on a frictionless axle. A second disk, of rotational inertia 1.0 kg·m² and not spinning, is dropped onto it and they turn together. What is their common angular speed? Wikipedia, "Angular momentum"; course topic 6.4
  • A playground platform with rotational inertia 200 kg·m² turns freely at 2.0 rad/s. A 25 kg child stands on it 2.0 m from the axis, then walks to the center. What is the new angular speed? Wikipedia, "Angular momentum" and Wikipedia, "Moment of inertia"; course topic 6.4
  • A spinning skater draws in her arms and legs, and no external torque acts on her. Which quantity stays the same? Wikipedia, "Angular momentum"; course topic 6.4
  • During a collision, disk A gives disk B an angular impulse of +3.0 kg·m²/s. What angular impulse does B give A? Wikipedia, "Angular momentum"; course topic 6.4
  • In that collision a 2.0 kg·m² disk at 6.0 rad/s joins a 1.0 kg·m² disk at rest, and they finish at 4.0 rad/s. How much kinetic energy is lost? Wikipedia, "Angular momentum" and Wikipedia, "Rotational energy"; course topic 6.4
  • While one spinning disk drags a second disk up to speed, for which system is the angular momentum constant? Wikipedia, "Angular momentum"; course topic 6.4

Topic 6.5: Rolling 6

  • A ball rolls down a ramp without slipping. A second, identical ball slides and spins down a slick ramp, slipping the whole way against kinetic friction. For which ball is mechanical energy conserved? Wikipedia, "Rolling"; course topic 6.5
  • A hoop and a solid sphere start together from rest at a ramp's top, and both roll without slipping. Which reaches the bottom first? Wikipedia, "List of moments of inertia" and Wikipedia, "Rolling"; course topic 6.5
  • A solid cylinder rolls without slipping down a ramp inclined at 30°. Taking g = 10 m/s², what is the acceleration of its center of mass? Wikipedia, "List of moments of inertia" and Wikipedia, "Rolling"; course topic 6.5
  • A thin hoop rolls without slipping. What fraction of its total kinetic energy is rotational? Wikipedia, "List of moments of inertia" and Wikipedia, "Rolling"; course topic 6.5
  • A wheel of radius 0.25 m rolls without slipping and turns at 8.0 rad/s. How fast does its center of mass move? Wikipedia, "Rolling"; course topic 6.5
  • A wheel rolls without slipping along level ground, its center moving at speed v. How fast, relative to the ground, are the point touching the ground and the point at the top of the wheel moving? Wikipedia, "Rolling"; course topic 6.5

Topic 6.6: Motion of orbiting satellites 3

  • A probe leaves a planet at exactly its escape speed, and afterward only the planet's gravity acts on it. What is the total mechanical energy of the probe and planet? Wikipedia, "Circular orbit" and Wikipedia, "Escape velocity"; course topic 6.6
  • A satellite is in a circular orbit, and the gravitational potential energy of the satellite and planet is −8.0 × 10⁹ J. What is the satellite's kinetic energy? Wikipedia, "Circular orbit"; course topic 6.6
  • A satellite moves around a planet in an elliptical orbit. Where is the satellite moving fastest? Wikipedia, "Elliptic orbit" and Wikipedia, "Kepler's laws of planetary motion"; course topic 6.6

How this list was compiled: Our own questions, written to Unit 5 (Torque and Rotational Dynamics) and Unit 6 (Energy and Momentum of Rotating Systems) of the College Board's AP Physics C: Mechanics Course and Exam Description, effective fall 2024, https://apcentral.collegeboard.org/media/pdf/ap-physics-c-mechanics-course-and-exam-description.pdf, read 2026-10-10. Every numeric answer is worked from the numbers the question prints, and each was worked out a second time on 2026-10-10. The principle behind each answer was read on 2026-10-10 in the Wikipedia article named under the question. Licence: Own work.

How it works

This AP Physics C rotational motion practice test follows the AP Physics C: Mechanics framework: 56 questions of our own on Unit 5 and Unit 6. It is unofficial and not affiliated with or endorsed by the College Board.

Read the full guide

What Units 5 and 6 cover

In the College Board's course description, read October 10, 2026, Unit 5 is Torque and Rotational Dynamics and Unit 6 is Energy and Momentum of Rotating Systems. The bank has a set for each of their twelve topics, from rotational kinematics to orbiting satellites, with three to six questions in each. The description gives topics no weights, so the spread is ours.

Numbers and sources

Every numeric answer is worked from the numbers the question prints, and each was worked out a second time. Under each answer is the Wikipedia article where the principle can be read.

  • Pick the axis first. Torque, rotational inertia and angular momentum all change with the axis you measure them about.
  • Rolling without slipping means v = Rω. Use it to turn every ω in an energy equation into v.
  • The description limits rotation directions to clockwise and counterclockwise. The vector directions of angular velocity and acceleration are not assessed.

Questions and answers

What unit is rotational motion in AP Physics C?

Two units of AP Physics C: Mechanics: Unit 5, Torque and Rotational Dynamics, and Unit 6, Energy and Momentum of Rotating Systems. Each carries 10 to 15% of the multiple-choice section, which has 42 questions in 85 minutes.

Does this work as an AP Physics 1 rotational motion practice test?

Mostly. AP Physics 1 has Units 5 and 6 under the same two names, without calculus. Three questions here need a derivative or an integral and one uses a cross product, which only Physics C asks for. The rest use algebra.

What is the rotational inertia of a rod, a disk and a hoop?

About the center, a thin rod has ML²/12, a solid disk ½MR² and a thin hoop MR². A rod about one end has ML²/3, by the parallel axis theorem. Physics C students are expected to derive the rod and the rings with calculus.

Are these real AP Physics exam questions?

No. The College Board owns the real questions, and none appears here, even in other words. Every question was written for this page from the topics the course description lists.

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