Essential University Physics: Volume 1 (3rd Edition)

Published by Pearson
ISBN 10: 0321993721
ISBN 13: 978-0-32199-372-4

Chapter 10 - Exercises and Problems - Page 185: 39


Please see the work below.

Work Step by Step

We know that the translational kinetic energy is given as $K_{t}=(\frac{1}{2})mv^2$ The rotational kinetic energy is given as $K_r=(\frac{1}{2})I\omega^2=(\frac{1}{2})(\frac{1}{2}mr^2)(\frac{v}{r^2})=\frac{1}{4}mv^2$ Now the total kinetic energy is given as $K_{total}=K_t+K_r=(\frac{1}{2})mv^2+(\frac{1}{4})mv^2=(\frac{3}{4})mv^2$ Now we can find the required ratio as $\frac{K_r}{K_{total}}=\frac{(\frac{1}{4})mv^2}{(\frac{3}{4})mv^2}=\frac{1}{3}$
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