Quick answer: Angular momentum is the rotational equivalent of momentum: L = Iω for a rigid body, or L = r × p for a particle. This AP Physics C test on angular momentum has 8 questions worth 20 marks, to do in 45 minutes: rolling relation, skater and hollow against solid. The mark scheme is on a separate page; free printable PDF.
This test covers angular momentum, conservation and rolling in the style of AP Physics C: Mechanics. Show every step of your working, give units and state any assumption. You may use a calculator and g = 9.81 m/s². Marks are shown for each part and the total is 20.
Level: AP Physics C (Mechanics and E&M, calculus-based) · Curriculum: AP PC:M Unit 6
Question 1 Rolling relation (2 marks)
A wheel of radius 0.25 m rolls without slipping at 6.0 m/s.- Calculate its angular speed. (1 mark)
- State the speed of the top of the wheel relative to the ground. (1 mark)
Question 2 Skater (3 marks)
A skater spins at 3.0 rad/s with I = 2.4 kg m². She pulls her arms in so that I = 1.2 kg m².- Calculate her new angular speed. (1 mark)
- Calculate the change in her kinetic energy. (1 mark)
- Explain where the extra energy comes from. (1 mark)
Question 3 Hollow against solid (2 marks)
Explain why a solid cylinder reaches the bottom of a slope before a hollow cylinder of the same mass and radius when both roll without slipping.Question 4 Rolling up a slope (3 marks)
Question 5 Friction and work (2 marks)
A ball rolls without slipping down a rough slope. Explain why static friction does no work on it even though it exerts a torque.Question 6 Two discs (3 marks)
A disc with I = 0.40 kg m² rotates at 10 rad/s. A second disc with I = 0.60 kg m², at rest, is dropped onto it on the same axis and they stick.- Calculate the final angular speed. (1 mark)
- Calculate the kinetic energy lost. (2 marks)
Question 7 Orbiting satellite (2 marks)
A satellite moves in an elliptical orbit around Earth. Explain why it moves fastest at its closest point.Question 8 Torque from L(t) (3 marks)
The angular momentum of a rotor is L = 4.0t³ kg m²/s, with t in seconds, and its moment of inertia is 6.0 kg m².- Calculate the net torque at t = 2.0 s. (1 mark)
- Calculate the angular speed at t = 2.0 s. (1 mark)
- State what the net torque is doing to L. (1 mark)
