Question

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.

Answer 1

Step-by-step explanation:

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