Qualitative/quantitative translation (QQT)

Dropping a disk onto a spinning disk

Unit 6
8 points
About 18 minutes

You can use a calculator on this question, just like on exam day.

A shorter multipart problem that connects reasoning in words with an equation. You make and justify a claim without equations, derive an equation from a physics principle, and then explain whether the two agree or use them to predict what happens in a changed situation. On the exam: Question 4 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 15–20 minutes.

The question

Disk 1, with rotational inertia I₁, spins freely at angular speed ω₀ on a vertical, frictionless axle. Disk 2, with rotational inertia I₂, is initially not rotating. Disk 2 is dropped onto disk 1 so that they share the same axle. Friction between the disks makes them slip briefly, and then they rotate together at a common angular speed ω_f.

Suggested time: 18 minutes

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Part (a)

3 points

(i) Is ω_f greater than, less than, or equal to ω₀? (ii) Does the total rotational kinetic energy of the two-disk system increase, decrease, or stay the same? Justify your answers. Do not use equations in this part; reason in words.

Your answer to part (a)

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Part (b)

3 points

Derive expressions for (i) ω_f and (ii) the ratio K_f/K_i of the final to the initial rotational kinetic energy, in terms of I₁, I₂, and ω₀, as appropriate.

Your answer to part (b)

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Part (c)

2 points

Use your expressions from part (b) to explain how they agree with your answers in part (a). Then predict what happens to ω_f and K_f/K_i if disk 2's rotational inertia is much smaller than disk 1's, and explain whether that makes physical sense.

Your answer to part (c)

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