Athin, very light wire is wrapped around a drum that is free to rotate. the free end of the wire is attached to a ball of mass m. the drum has the same mass m. its radius is r and its moment of inertia is i = (1/2)mr2. as the ball falls, the drum spins. at an instant that the ball has translational kinetic energy k, what is the rotational kinetic energy of the drum?

K/2

Rotational kinetic energy can be expressed as: k (rotational) = 1/2 Iw2 

where w is the angular velocity, I is the moment of inertia around the axis of rotation.

K=1/2mv2

Kdrum=1/2 Iw2=1/2(1/2mR2) (v/R)2 =1/4 mv2 = 1/2K or K/2

The energy due to the rotation of an object and is part of its total kinetic energy is called rotational kinetic energy. Things that spool without sliding have some fraction of their energy as translational kinetic and the remainder as rotational kinetic and looking at rotational energy separately around an object’s axis of rotation yields the ratio that depends on the moment of inertia of the object that is rolling.