Discussion
The dimensional formula for the product of moment of inertia and the square of angular velocity is
Answer: D
The dimensional formula is \(ML^{2}T^{-2}\).
Moment of inertia is mass times distance squared, \([ML^{2}]\), and angular velocity is per unit time, \([T^{-1}]\):
\[ [I\omega^{2}] = [ML^{2}][T^{-2}] = [ML^{2}T^{-2}] \]
This is the dimension of energy, as expected, since rotational kinetic energy is \(\frac{1}{2}I\omega^{2}\). \(ML^{2}T^{-1}\) is angular momentum \(I\omega\), \(MLT^{-2}\) is force, \(MLT^{-1}\) is linear momentum, and \(ML^{0}T^{-2}\) drops the length dimension.
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