Qualitative/quantitative translation (QQT)

Ball striking a hanging rod: sticking vs bouncing

Units 5 and 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. 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 15–20 minutes. This question type started in May 2025, so Physics C: Mechanics free-response questions from 2024 and earlier are built differently.

The question

A uniform rod of mass M and length L hangs vertically at rest from a frictionless pivot at its upper end. Its rotational inertia about the pivot is $\tfrac{1}{3}ML^2$ . A small ball of mass m moves horizontally with speed v and strikes the lower end of the rod, perpendicular to the rod. In Case 1, the ball is made of clay and sticks to the rod. In Case 2, the ball is made of rubber and bounces straight back with speed v/2. The ball's mass is much smaller than the rod's (less than one-ninth of it), so the rebound in Case 2 is physically possible. A student claims: “In Case 1 the rod will start rotating faster, because the clay stays with the rod and gives it all of its momentum.”

Suggested time: 18 minutes

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Part (a)

3 points

Do you agree or disagree with the student's claim about which case gives the rod the greater angular speed just after the collision? Justify your answer without using equations.

Your answer to part (a)

Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).

0 / 2,500 characters

Part (b)

3 points

Derive expressions for the rod's angular speed just after the collision in Case 1, $\omega_1$ , and in Case 2, $\omega_2$ , in terms of m, M, v, and L, as appropriate.

Your answer to part (b)

Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).

0 / 2,500 characters

Part (c)

2 points

Explain how your expressions from part (b) support your answer to part (a). Then determine the ratio $\dfrac{\omega_2}{\omega_1}$ when the ball's mass is small compared with the rod's (m ≪ M).

Your answer to part (c)

Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).

0 / 2,500 characters

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