Physics (10th Edition)

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

Chapter 9 - Rotational Dynamics - Problems - Page 246: 40



Work Step by Step

1) Find the angular acceleration of the dart We know the initial tangential speed of the dart $v_0=0$, the final speed $v_T=5m/s$ and $t=0.1s$. The tangential acceleration of the dart is $$a_T=\frac{v_T-v_0}{t}=50m/s^2$$ The radius of rotation is $r=0.28m$. We can find the angular acceleration using $$\alpha=\frac{a_T}{r}=178.57rad/s^2$$ 2) The torque required to help the dart to have $\alpha=178.57rad/s^2$ is $$\tau=I\alpha=(0.065kg.m^2)(178.57rad/s^2)=11.61N.m$$ This torque is produced by $M$ and has a lever arm of $0.025m$. Therefore, $$M=\frac{\tau}{0.025m}=464N$$
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