The rotational kinetic energy of an object is given by
[tex]E= \frac{1}{2} I \omega^2[/tex]
where I is the moment of inertia of the object and [tex]\omega[/tex] its angular speed.
Re-arranging the formula, we find
[tex]I= \frac{2E}{\omega^2} [/tex]
and by using [tex]E=64 J[/tex] and [tex]\omega=10 rad/s[/tex], we find
[tex]I= \frac{2 \cdot 64 J}{(10 rad/s)^2}=1.28 J s^2 [/tex]
