# Chapter 8 - Rotational Motion - Questions: 10

The ball will have the same speed at the bottom of each incline.

#### Work Step by Step

Assuming that friction does no work, we may apply conservation of energy to the process. The energy at the top equals the energy at the bottom of the incline. $$E_{top} = E_{bottom}$$ $$mgh = \frac{1}{2}mv^{2}+ \frac{1}{2}I \omega^2$$ If the ball rolls without slipping then $\omega = \frac{v}{R}$. The speed at the bottom depends only on the height of the incline, not on the angle of inclination.

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