# A friend incorrectly says that a body cannot be rotating when the net torque acting on it is...

## Question:

A friend incorrectly says that a body cannot be rotating when the net torque acting on it is zero. What is the correct statement?

1. The original statement made by the friend is actually correct.

2. Once a body startsrotatingthenet torque is zero.

3. A body's angular velocity cannot change if the net torque acting on it is zero and the moment of inertia does not change.

4. A body can have an angular velocity only when a non-zero net torque is acting on it.

## Torque:

Just like Force describes a push/pull which changes the state of rest or linear motion of an object, the torque is a quantity of similar nature for circular motion. It can be thought of as a twisting/turning force.

It is numerically equal to the product of force and the arm length at which the force is acting and in the language of the law of motion of Newton, it is equal to the rate of change of angular momentum of a rotating body just like force is the rate of change of linear momentum of a body.

Newton's 2nd law of motion states that the state of rest or of motion of an object does not change unless and until an external force acts on it.

Torque is a quantity analogous to force for rotational motion.

1)

The original statement made by the friend is "A body cannot be rotating when the net torque acting on it is zero". For linear motion, this statement translates to "A body cannot be moving when the net force acting on it is zero". Clearly, this statement is incorrect as the force only changes the state of rest or of motion.

2)

"Once the body starts rotating, the net torque is zero". This translates to " Once a body starts moving, the net force acting on it zero". This statement is also incorrect as a force can act on both stationary as well as moving objects.

3)

"A body's angular velocity cannot change if the net torque acting on it is zero and the moment of inertia does not change ". This statement translates to "A body's velocity cannot change if the net torque acting on it is zero and the mass of the body does not change. "

This is the statement of Newton's First Law. Therefore this statement is correct.

4)

"A body can have an angular velocity only when a non-zero net torque is acting on it". This statement translates to "A body can have a velocity only when a non-zero net force is acting on it".

A moving object will continue its state of motion as long as it remains unaffected by an external force. This statement is also incorrect.