## College Physics (4th Edition)

Published by McGraw-Hill Education

# Chapter 10 - Conceptual Questions - Page 395: 11

#### Answer

The motion of the shadow is not SHM.

#### Work Step by Step

Let $t=0$ when the plane is at the bottom of the circle and let $\theta = 0$ be the angle at the bottom of the circle. Let $R$ be the radius of the circle that the plane follows. Let $x$ be horizontal component of the plane's position around the circle. Let $x = 0$ be the center of the circle. We can find an expression for $x$ in terms of time $t$: $\frac{x}{R} = sin~\theta$ $x = R~sin~\theta$ If the angular speed was constant, we could describe the position $x$ with the equation $x = R~sin~(\omega~t)$. However, since the angular speed is not constant, we can not express $x$ in this form. Therefore, the motion of the shadow is not SHM.

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