**AP Physics 1 Question 121: Answer and Explanation**

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**Question: 121**

**1.**

Three wagons each have the same total mass (including that of the wheels) and four wheels, but the wheels are differently styled. The structure, mass, and radius of each wagon’s wheels are shown in the preceding chart. In order to accelerate each wagon from rest to a speed of 10 m/s, which wagon requires the greatest energy input?

- A. Wagon A
- B. Wagon B
- C. Wagon C
- D. All require the same energy input

**Correct Answer:** B

**Explanation:**

**B**-The energy input must be enough to change the translational kinetic energy of the cart *and* to change the rotational kinetic energy of the wheels. Since all carts have the same mass and change speed by the same amount, they all require the same energy input to change the translational KE. Whichever wheels have the largest rotational inertia will require the largest energy input to get to the same speed. Calculating, wagon B has the largest rotational inertia of 0.004 kg·m^{2}.