## College Physics (4th Edition)

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