Answer
a. Yes.
b. Yes.
Work Step by Step
a. Imagine a merry-go-round that is pushed at its rim, in a tangential direction. The net force on the object is zero, because the object’s center of mass stays in place. However, there is a net torque, and the merry-go-round has an angular acceleration. The object is in translational equilibrium but not rotational equilibrium.
b. Imagine a uniform rod that is dropped from a tall building. The net torque on the rod is zero because gravity is acting at its very center. Its angular velocity does not change. However, the net force causes its center of mass to accelerate. The object is in rotational equilibrium but not translational equilibrium.
