Chapter 8.3, Problem 42SSC

(a)

To determine

The example of an object which is in rotational equilibrium, but not in translational equilibrium.

Explanation of Solution

Introduction:

Translational equilibrium: The object is said to be in translational equilibrium if the resultant of all forces acting on an object is zero. In this equilibrium, the center of mass of the object stays either at rest or moves with uniform speed.

Rotational equilibrium: The body is said to be in rotational equilibrium if the resultant of all the torque acting on an object is zero. In this equilibrium, the angular velocity of the object does not change.

  

Since the same forces are in same direction and both applied at equal distance from the center; the net torque is zero which leads to rotational equilibrium. But the net force on the object is in downward direction and hence accelerated downwards which leads to translational motion.

(b)

To determine

The example of an object which is in translational equilibrium, but not in rotational equilibrium.

Explanation of Solution

Introduction:

Translational equilibrium: The object is said to be in translational equilibrium if the resultant of all forces acting on an object is zero. In this equilibrium, the center of mass of the object stays either at rest or moves in uniform motion.

 Rotational equilibrium: The body is said to be in rotational equilibrium if the resultant of all the torque acting on an object is zero. In this equilibrium, the angular velocity of the object does not change.

  

As shown above, a fan is pivoted at its center hence it cannot move in translational motion hence it is in translational equilibrium. But it rotates about the pivoted point on exerting two forces at different points on the fan in opposite direction which leads to net torque to be non-zero and hence, it is in rotational motion.