Kinetic Energy of Rotation

To calculate the kinetic energy of a rotating object we add up all of the kinetic energies of the individual particles making up the object, namely

The speeds are . Note we do not write  because the rotational velocity of all particles is the same value . That is ₁ = ₂ = ₃ =…..≡. Substituting gives

Define rotational inertia or rotational mass as

and we get

which looks exactly like   where instead of velocity v we have  and instead of mass (or inertia) m we have rotational mass (or rotational inertia) I. Recall that mass, or inertia, tells us how difficult it is to move an object. Similarly the rotational mass, or rotational inertia, tells us how difficult it is to rotate an object.