**AP Physics 1 Question 176: Answer and Explanation**

### Test Information

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**Question: 176**

**6.**

Question below refers to the following information:

A small ball of mass *m* moving to the right at speed *v* collides with a stationary rod, as shown in the figure. After the collision, the ball rebounds to the left with speed *v*_{1}, while the rod’s center of mass moves to the left at speed *v*_{2}. The rod also rotates counterclockwise.

Which of the following equations determines the rod’s change in angular momentum about its center of mass during the collision?

- A.
*Iω*where*I*is the rod’s rotational inertia about its center of mass, and*ω*is its angular speed after collision. - B.
*Iv*_{2}*/r*, where*I*is the rod’s rotational inertia about its center of mass, and*r*is half the length of the rod. - C.
*mv*_{1}*d*, where*d*is the distance between the line of the ball’s motion and the rod’s center of mass. - D.
*mv*_{1}*r*, where*r*is half the length of the rod.

**Correct Answer:** A

**Explanation:**

**A**-The rod starts from rest, so its final angular momentum is the same as its change in angular momentum. Although the equation *ω* = *v/r* is valid for a point object moving in a circle, it does not apply to a rotating rod; thus, choice B is wrong. Choice C gives the final angular momentum of the ball, which is not the same as the angular momentum change of the rod because the ball does NOT start from rest.