Physics: Principles with Applications (7th Edition)

Published by Pearson
ISBN 10: 0-32162-592-7
ISBN 13: 978-0-32162-592-2

Chapter 8 - Rotational Motion - Problems - Page 224: 42

Answer

The mass of the sphere is 23 kg.

Work Step by Step

We first find the angular acceleration $\alpha$: $\theta = \frac{1}{2}\alpha t^2$ $\alpha = \frac{2\theta}{t^2} = \frac{(2)(2\pi~rad/rev)(160~rev))}{(15.0~s)^2}$ $\alpha = 8.936~rad/s^2$ Then, we find the moment of inertia $I$: $\tau = I~\alpha$ $I = \frac{\tau}{\alpha} = \frac{10.8~m\cdot N}{8.936~rad/s^2} = 1.21~kg\cdot m^2$ Then, we find the mass of the sphere: $I = \frac{2}{5}MR^2$ $M = \frac{5I}{2R^2} = \frac{(5)(1.21~kg\cdot m^2)}{(2)(0.36~m)^2}$ $M = 23~kg$ The mass of the sphere is 23 kg.
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