**AP Physics 1 Question 140: Answer and Explanation**

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**Question: 140**

**10.** A solid sphere (*I* = 0.06 kg·m^{2}) spins freely around an axis through its center at an angular speed of 20 rad/s. It is desired to bring the sphere to rest by applying a friction force of magnitude 2.0 N to the sphere’s outer surface, a distance of 0.30 m from the sphere’s center. How much time will it take the sphere to come to rest?

- A. 4 s
- B. 2 s
- C. 0.06 s
- D. 0.03 s

**Correct Answer:** B

**Explanation:**

**B**-This is a calculation using *τ*_{net} = *Iα*. The net torque on the sphere is force times distance from the center, or (2.0 N)(0.30 m) = 0.60 m·N. Now the angular acceleration can be calculated: (0.60 m·N) = (0.06 kg·m^{2})(*α*), so *α* = 10 rad/s per second. Use the definition of angular acceleration: the sphere loses 10 rad/s of speed each second. It started with 20 rad/s of speed, so after 1 s it has 10 rad/s of speed; after 2 s it will have lost all its speed.