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 lab on angular momentum gives the aim, the equipment, the safety points, a step-by-step method, sample results and 7 analysis questions; the answers are on a separate page and the lab sheet is a free printable PDF.
A solid cylinder and a hollow tube are released together on a ramp. Which one wins, and by how much? This lab measures the rolling acceleration of both and turns it into a measurement of the moment-of-inertia factor β, testing the energy argument from the lesson with simple equipment.
Level: AP Physics C (Mechanics and E&M, calculus-based) · Curriculum: AP PC:M Unit 6
Aim
To measure the acceleration of a solid cylinder and of a hollow tube rolling down the same ramp, and to use it to find the shape factor β in I = βmR².
Equipment
- A smooth wooden board 1.20 m long
- A solid aluminium rod and a thin-walled aluminium tube of the same outer diameter
- Books to raise one end, a metre rule, masking tape for marks
- A stopwatch or phone timer
Safety
Stand the ramp on a non-slip surface and keep feet clear of the bottom end. Place a cushion or box at the end to stop the rollers, and do not release them towards other people.
Method
- Raise one end of the board by 0.12 m using books and measure the board length to find sinθ = 0.12 / 1.20 = 0.100.
- Mark a start line and a stop line 1.00 m apart along the board.
- Release the solid rod from rest at the start line without pushing it and time it to the stop line.
- Repeat five times, then do the same with the hollow tube.
- Calculate the mean time for each and use a = 2s / t² with s = 1.00 m.
Results
Sample measurements for a ramp with sinθ = 0.100:
| Trial | Solid aluminium rod: t (s) | Hollow tube: t (s) |
|---|---|---|
| 1 | 1.76 | 2.03 |
| 2 | 1.73 | 2.00 |
| 3 | 1.78 | 2.05 |
| 4 | 1.75 | 2.02 |
| 5 | 1.74 | 2.04 |
| Mean | 1.752 | 2.028 |
Analysis questions
Question 1 Mean time and spread
Check the means in the table. State the range of the solid-rod times and the uncertainty in its mean time.Question 2 Acceleration
Calculate the acceleration of each roller from a = 2s / t² and the percentage uncertainty in the solid rod’s value.Question 3 Experimental shape factor
Use a = g sinθ / (1 + β) to find β for each roller.Question 4 Compare with theory
State the theoretical β for each roller and compare your values.Question 5 Ratio of accelerations
Calculate a_solid / a_tube and compare with the theoretical ratio.Question 6 Effect of mass
Explain whether the rod would reach the bottom sooner if its mass were doubled.Question 7 Improving the lab
Suggest two improvements that would reduce the uncertainty.
