College Physics (4th Edition)

Published by McGraw-Hill Education
ISBN 10: 0073512141
ISBN 13: 978-0-07351-214-3

Chapter 8 - Problems - Page 310: 1

Answer

The dimensions of $\frac{1}{2}I~\omega^2$ are $[M][L]^2~[T]^{-2}$, which are the dimensions of energy.

Work Step by Step

$I$ is rotational inertia and it has dimensions $[M][L]^2$, where $[M]$ is mass and $[L]$ is length. $\omega$ is angular velocity and it has dimensions $[T]^{-1}$ where $[T]$ is time. We can find the dimensions of $\frac{1}{2}I~\omega^2$: $([M][L]^2)~([T]^{-1})^2 = [M][L]^2~[T]^{-2}$ Note that these are the dimensions of energy.
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