Consider a rigid body that rotates but whose center of mass is at rest. a. Trueb. false: the rotational kinetic energy of the entire object is equivalent to the sum of the translational kinetic energy of each small piece of the object.

True

It is correct as the total rotational energy is the sum of transnational kinetic energy of each small piece of the object.

Consider a rigid body made of small particles each of mass dm have same angular velocity ω and the radius of the rotational path is r.

The velocity of each particle is v = r ω

So, the kinetic energy of each particle is

dK = 0.5 dm x v² = 0.5 x dm x r² x ω²

The total kinetic energy

K = 0.5 x I ω²

where, I is the moment of inertia