Question

If an object's rotational kinetic energy is 64 j and it rotates with an angular speed of 10 radians/s, what is its moment of inertia?

Answer 1

The rotational kinetic energy of an object is given by
$E= \frac{1}{2} I \omega^2$
where I is the moment of inertia of the object and $\omega$ its angular speed.

Re-arranging the formula, we find
$I= \frac{2E}{\omega^2}$
and by using $E=64 J$ and $\omega=10 rad/s$, we find
$I= \frac{2 \cdot 64 J}{(10 rad/s)^2}=1.28 J s^2$