Q. If $I$ is the moment of inertia and $\omega$ the angular velocity, what is the dimensional formula of rotational kinetic energy $\frac{1}{2}I\omega^{2}$?
A) $\lbrack ML^{2}T^{- 1}\rbrack$
B) $\lbrack M^{2}L^{- 1}T^{- 2}\rbrack$
C) $\lbrack ML^{2}T^{- 2}\rbrack$
D) $\lbrack M^{2}L^{- 1}T^{- 2}\rbrack$
Explanation
Do not think in terms of $I$ and $\omega$. Remember; kinetic energy is fundamentally ‘work’ $W =$Force $\times$ distance $= \left\lbrack MLT^{- 2} \right\rbrack \times \lbrack L\rbrack$ $= \lbrack ML^{2}T^{- 2}\rbrack$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.