Quick answer: Moment of inertia is I = ∫r² dm, the sum of each mass element times the square of its distance from the rotation axis. This AP Physics C test on moment of inertia has 8 questions worth 20 marks, to do in 45 minutes: moment of inertia, rod by integration and parallel axis. The mark scheme is on a separate page; free printable PDF.
This test covers moment of inertia by integration, the parallel axis theorem, torque, rotational dynamics and conservation of angular momentum. Show your working and give units. Use g = 9.81 m/s². The time limit is 45 minutes and you may use a calculator.
Level: AP Physics C (Mechanics and E&M, calculus-based) · Curriculum: AP PC:M Unit 5
Question 1 Moment of inertia (2 marks)
- Define the moment of inertia of a body about an axis. (1 mark)
- State the equation that links net torque, moment of inertia and angular acceleration. (1 mark)
Question 2 Rod by integration (3 marks)
A uniform rod of mass 0.50 kg and length 0.60 m rotates about an axis perpendicular to it through one end.- Write dm in terms of dx. (1 mark)
- Evaluate I = ∫x² dm. (1 mark)
- Calculate I. (1 mark)
Question 3 Parallel axis (3 marks)
The same rod has Icm = ML²/12 about its centre.- Calculate Icm. (1 mark)
- State the parallel axis theorem. (1 mark)
- Calculate I about a parallel axis 0.20 m from the centre. (1 mark)
Question 4 Pulley and mass (4 marks)
A 1.5 kg mass hangs from a rope wrapped around a solid disc pulley of mass 2.0 kg and radius 0.10 m, as shown.- Write the equations of motion for the mass and for the pulley. (1 mark)
- Calculate the acceleration of the mass. (1 mark)
- Calculate the tension in the rope. (1 mark)
- Calculate the angular acceleration of the pulley. (1 mark)
Question 5 Braking a flywheel (3 marks)
A flywheel with I = 0.80 kg·m² spins at 50 rad/s. A brake applies a constant torque of 20 N·m.- Calculate the angular deceleration. (1 mark)
- Calculate the time to stop. (1 mark)
- Calculate the kinetic energy removed. (1 mark)
Question 6 Hoop and disc (2 marks)
A hoop and a solid disc of equal mass and radius are released together from rest at the top of an incline and roll without slipping. State which reaches the bottom first and explain using moment of inertia. (2 marks)Question 7 Spinning skater (2 marks)
Explain, using angular momentum, why a skater spins faster when she pulls her arms in, and calculate the factor if her moment of inertia halves. (2 marks)Question 8 Disc formula (1 mark)
State the moment of inertia of a uniform solid disc of mass M and radius R about its central axis. (1 mark)
