Chapter 11, Problem 1DQ

To determine

Whether a rigid object in uniform rotation satisfies the first and second condition of equilibrium and it means that all the particles are in equilibrium state.

Answer to Problem 1DQ

Thus, a uniform rotating rigid body obeys second condition of equilibrium, but not the first condition. Equilibrium state of a rigid body does not guarantee the equilibrium state of each and every particle of rigid body.

Explanation of Solution

Consider the rigid body in uniform rotation. Uniform rotation means that the object moves with constant angular velocity. So the angular acceleration of body remains zero. Torque is determined by the mass and angular acceleration of the body. This means that the net torque acting on the body is zero. So the system satisfies the second condition of equilibrium.

An object moves with constant angular velocity cannot have a constant value of linear velocity. This is because, even its magnitude is same, continues change in direction will produce acceleration. Accelerating body must have a non-zero value of force. This means that object will not satisfy the first condition.

A rigid body with zero value of net torque does not mean that each and every particle is in rotational equilibrium. Torque is a vector quantity. The only condition for zero net torque is that the vector sum of all clockwise torques should be cancelled by the vector sum of all counterclockwise torques.

Conclusion: Thus, a uniform rotating rigid body obeys second condition of equilibrium, but not the first condition. Equilibrium state of a rigid body does not guarantee the equilibrium state of each and every particle of rigid body.