Experimental design and analysis (LAB)

Rotational inertia of a wheel

Unit 5
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. Section II has 4 questions in 95 minutes (50% of the exam score), one of each type in this order; calculator allowed. The CED suggests 25–30 minutes.

The question and its sources

Students want to determine the rotational inertia of a wheel mounted on a fixed horizontal axle. A string can be wrapped around the wheel's hub, which has radius 0.050 m. The axle has a small amount of friction.

Part A: Available equipment

The wheel on its axle, string, a set of hanging masses with a hook, a meterstick, a stopwatch, and an electronic balance.

Source: Hypothetical lab setup

Part B: Table 1. Another group's data (a force sensor pulls the string tangent to the hub with a constant force; a rotary motion sensor measures the angular acceleration)

Force on the string F (N)	Angular acceleration α (rad/s²)
0.50	5.2
1.00	11.0
1.50	17.8
2.00	23.5
2.50	30.2

Source: Hypothetical data

Suggested time: 27 minutes

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Part (A(i))

3 points

Describe an experimental procedure, using only the equipment in Part A, to collect data that would allow you to determine the wheel's rotational inertia. Include what you would measure and how you would find the wheel's angular acceleration.

Your answer to part (A(i))

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Part (A(ii))

2 points

Describe how you would use your data to determine the rotational inertia, taking into account the friction in the axle.

Your answer to part (A(ii))

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Part (B(i))

1 point

Using Table 1, indicate which quantities you would graph to produce a straight line whose slope gives the wheel's rotational inertia, and calculate any values you need.

Your answer to part (B(i))

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Part (B(ii))

2 points

Plot 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 (list their values), and the best-fit line.

Your answer to part (B(ii))

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Part (B(iii))

2 points

Use your best-fit line to determine the rotational inertia of the wheel, and explain the physical meaning of the line's vertical intercept.

Your answer to part (B(iii))

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