Quick answer: Angular momentum is L = Iω, and it stays constant when no net external torque acts, so a spinner who pulls mass inward spins faster. This AP Physics 1 test on angular momentum has 8 questions worth 20 marks, to do in 45 minutes: definitions, flywheel and spinning skater. The mark scheme is on a separate page; free printable PDF.
This test covers rotational kinetic energy, rolling motion and conservation of angular momentum. Show all working, give units and justify your reasoning. A calculator is allowed.
Level: AP Physics 1 (algebra-based) · Curriculum: AP P1 Unit 6
Question 1 Definitions (2 marks)
- State the equation for the angular momentum of a rigid object rotating about a fixed axis. (1 mark)
- State the condition under which the angular momentum of a system is conserved. (1 mark)
Question 2 Flywheel (2 marks)
A flywheel has rotational inertia 0.80 kg m² and angular speed 25 rad/s.- Calculate its rotational kinetic energy. (1 mark)
- Calculate its angular momentum. (1 mark)
Question 3 Spinning skater (3 marks)
A skater with I = 3.0 kg m² spins at 2.4 rad/s, then draws in her arms so that I = 1.2 kg m². There is no external torque.- Calculate her final angular speed. (2 marks)
- State and explain what happens to her kinetic energy. (1 mark)
Question 4 Rolling cylinder (3 marks)
A solid cylinder of mass 2.0 kg rolls without slipping at 4.0 m/s. Its rotational inertia is ½MR².- Calculate its translational kinetic energy. (1 mark)
- Calculate its rotational kinetic energy. (1 mark)
- Calculate its total kinetic energy. (1 mark)
Question 5 Racing down a ramp (3 marks)
A hoop and a solid disk of equal mass and radius are released together from rest at the top of the ramp shown. Both roll without slipping.- State which reaches the bottom first. (1 mark)
- Use energy ideas to explain your answer. (2 marks)
Question 6 Clay lump on a turntable (3 marks)
A turntable with I = 0.20 kg m² spins at 6.0 rad/s. A clay lump adds 0.050 kg m² to the rotational inertia when it sticks to the turntable.- Calculate the final angular speed. (2 marks)
- Calculate the kinetic energy lost. (1 mark)
Question 7 Work by a torque (2 marks)
A constant torque of 3.0 N m turns a wheel through 8.0 rad. The wheel starts from rest and has I = 0.30 kg m².- Calculate the work done by the torque. (1 mark)
- Calculate the final angular speed. (1 mark)
Question 8 Ball up a slope (2 marks)
A solid ball (I = (2/5)mR²) rolls without slipping at 3.5 m/s on level ground and then up a smooth-surfaced slope. Calculate the maximum vertical height it reaches. (2 marks)
