## Rotational vs Translational Kinetic Energy

$$E_{rotational} = \frac1 2 I*\omega^2$$

Consider a particle with mass $m$ revolving about a pivot $O$ with a constant distance $r$ between them. It is revolving with constant angular velocity $\omega$
Its moment of inertia is:
$$I = m*r^2$$
Thus
$$E_{rotational} = \frac1 2 m*r^2*\omega^2$$

Since $\omega = \frac v r$

$$E*{rotational} = \frac1 2 m r^2\frac{v^2}{r^2}$$
$$E*{rotational} = \frac1 2 m*v^2$$

We could see this looks exactly as the Translational Kinetic Energy, which is:

Of an any given moment, the instantaneous velocity of this particle is $v$, so we can calculate its Translational Kinetic Energy with the formula

$$E_{translational} = \frac1 2 m*v^2$$