Question

Express the equation of kinetic energy of a rotating body in terms of its angular momentum and angular velocity. ​

Answer 1

Equation of kinetic energy:

• Rotational Kinetic Energy is represented as :

• I is moment of inertia and $\omega$ is angular velocity.

$KE = \dfrac{1}{2} I { \omega}^{2}$

$\implies KE = \dfrac{1}{2} (I \times \omega) \times \omega$

• $I\times\omega$ is angular momentum = L

$\implies KE = \dfrac{1}{2} \times L \times \omega$

So, final answer is:

$\boxed{ KE = \dfrac{1}{2} \times L \times \omega}$