Physics (10th Edition)

Published by Wiley
ISBN 10: 1118486897
ISBN 13: 978-1-11848-689-4

Chapter 8 - Rotational Kinematics - Problems - Page 213: 25


a) $t=10s$ b) $\alpha=-2rad/s^2$

Work Step by Step

We have: initial velocity $\omega_0=+20rad/s$, final speed $\omega=0$ and displacement $\theta=+15.92rev\times\Big(\frac{2\pi rad}{1rev}\Big)=100rad$ a) The amount of time it takes for the bike to stop is $$\theta=\Big(\frac{\omega+\omega_0}{2}\Big)t$$ $$t=\frac{2\theta}{\omega+\omega_0}=10s$$ b) The angular acceleration of each wheel is $$\alpha=\frac{\omega-\omega_0}{t}=-2rad/s^2$$
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