Experimental design and analysis (LAB)
Rotational inertia of a disk from dropped rings
- Units 5 and 6
- 10 points
- About 27 minutes
You can use a calculator on this question, just like on exam day.
A two-part lab question. First you design an experiment to answer a question: what you change, what you measure, the equipment and how you would analyze the data. Then you get a data table from a similar experiment, choose what to graph (often so the points fall on a straight line), plot it and use the slope, the intercept or the graph's shape to answer a question. On the exam: Question 3 of 4. New for May 2027: the free-response section is 95 minutes, down from 100, for all 4 questions (50% of your score), one of each type in this order. Calculator and equation sheet allowed. The CED suggests 25–30 minutes. This question type started in May 2025, so Physics C: Mechanics free-response questions from 2024 and earlier are built differently.
The question and its sources
Students want to determine the rotational inertia of a horizontal disk that spins on a vertical, low-friction axle. They plan to use rotational collisions: a thin ring is held just above the spinning disk, centered on the axle, and dropped so it lands on the disk and quickly spins along with it.
Part A: Available equipment
A horizontal disk on a vertical low-friction axle, with a rotary motion sensor on the axle that records angular speed against time; a set of thin metal rings that all have the same radius but different masses, each with an inner hole that fits loosely around the axle; a balance; and a ruler.
Source: Hypothetical lab setup
Part B: Table 1. Angular speed of the disk just before and just after each ring lands (ring radius 0.10 m)
| Ring mass m (kg) | ω₀ before (rad/s) | ω_f after (rad/s) |
|---|---|---|
| 0.050 | 30.2 | 24.0 |
| 0.100 | 29.6 | 19.9 |
| 0.150 | 31.0 | 17.6 |
| 0.200 | 30.4 | 15.3 |
| 0.250 | 29.8 | 13.1 |
Source: Hypothetical data
Suggested time: 27 minutes
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Part (A(i))
3 pointsUsing only the equipment listed in the setup, describe an experimental procedure you could use to collect data that would allow you to determine . Include what you would measure and how, what you would vary, and one step you would take to reduce experimental uncertainty.
Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).
0 / 2,500 characters
Part (A(ii))
2 pointsDescribe how you would use your data to determine . Include what you would graph and how you would use the graph.
Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).
0 / 2,500 characters
Part (B(i))
1 pointAnother group used rings of radius R = 0.10 m and collected the data in Table 1. Indicate which quantities you would graph to produce a straight line that could be used to determine . Calculate the values you would plot.
Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).
0 / 2,500 characters
Part (B(ii))
2 pointsPlot the quantities you chose and draw a best-fit line. You can't draw here, so describe the graph you would draw: what goes on each axis (with units), the scale, the points you would plot, and the best-fit line.
Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).
0 / 2,500 characters
Part (B(iii))
2 pointsUsing your best-fit line, calculate an experimental value for .
Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).
0 / 2,500 characters
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