## College Physics (4th Edition)

Published by McGraw-Hill Education

# Chapter 8 - Problems - Page 310: 3

#### Answer

(a) The mass of the child's ball is reduced by a factor of $\frac{1}{8}$ (b) The rotational inertia of the child's bowling ball is reduced by a factor of $\frac{1}{32}$

#### Work Step by Step

(a) $V = \frac{4}{3}\pi~R^3$ If the radius of the child's ball is decreased by a factor of $\frac{1}{2}$, then the volume is decreased by a factor of $(\frac{1}{2})^3 = \frac{1}{8}$ Then the mass of the child's ball is reduced by a factor of $\frac{1}{8}$ (b) We can write an expression for the rotational inertia of the adult's bowling ball: $I_a = \frac{2}{5}MR^2$ We can write an expression for the rotational inertia of the child's bowling ball: $I_c = \frac{2}{5}(\frac{M}{8})(\frac{R}{2})^2$ $I_c = \frac{1}{32}\times \frac{2}{5}MR^2$ $I_c = \frac{1}{32}\times I_a$ The rotational inertia of the child's bowling ball is reduced by a factor of $\frac{1}{32}$.

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