Dimensional Analysis of Rotational Quantities

Quantity	Expression	Dimensions
Angular velocity	omega = d $\frac{theta}{dt}$	[ $T^{-1}$ ]
Angular acceleration	alpha = d $\frac{omega}{dt}$	[ $T^{-2}$ ]
Torque	tau = r x F	[ $ML^{2T}^{-2}$ ]
MOI	I = $mr^2$	[ $ML^2$ ]
Angular momentum	L = I*omega	[ $ML^{2T}^{-1}$ ]
Rotational KE	$\frac{1}{2}$ I* $omega^2$	[ $ML^{2T}^{-2}$ ]

Note: Torque and work/energy have the same dimensions [ $ML^{2T}^{-2}$ ] but are physically different quantities. Torque is a vector (cross product); energy is a scalar.