# Is it necessary for force to be zero for constant angular velocity? [closed]

According to a few articles I read, they say Newton's first law for rotational inertia is that if net torque on body is zero it keeps on rotating with same angular velocity .

But will the body rotating with constant angular velocity can have zero force (by force I mean net force on the body hence only external force) also? I know the necessary and sufficient condition for angular velocity to be zero is that torque acting on it must be zero but My question is when the torque is zero is there a force acting on the the body because if torque is zero it is not necessary that force is also zero ? ie in other words if torque is zero that means body rotates with constant angular velocity but is there a force MAINTAINING this constant angular velocity or is it just like inertia in linear motion ?

(Also the body is rotating about a fixed axis and is rigid)

• Your wording is somewhat confusing. 0 net torque is the requirement to ensure it has a constant angular velocity. – JMac May 4 '17 at 10:55
• If a force is applied to the center of gravity, it will not exert torque on the body, hence the angular momentum will stay constant. – noah May 4 '17 at 10:57
• I have edited my question I hope now its clear – Matt May 4 '17 at 11:02
• @Michael okay but if torque is zero that means body rotates with constant angular velocity but is there a force MAINTAINING this constant angular velocity or is it just like inertia in linear motion ? – Matt May 4 '17 at 11:10
• It is just like inertia. – noah May 4 '17 at 11:11

Think of angular velocity $\omega$, angular acceleration $\alpha$, moment-of-inertia $I$ and torque $\tau$ in the exact same way as you think of normal (translational) velocity $v$, acceleration $a$, inertia (mass) $m$ and force $F$. They have their two equivalent laws combining them:

$$\sum F=ma\qquad , \qquad \sum \tau=I\alpha$$

And you can trust these laws.

• If there is a net torque $\sum \tau$, there is an angular acceleration $\alpha$. Regardless of what else is happening at the same time.

• Just like, if there is a net force $\sum F$ then there is an (translational) acceleration $a$. Regardless of other simultaneous effects and things.

So for example: If a force pushes at a point on an object that does not cause a torque, or if it causes a balanced torque, then there is zero net torque and no angular acceleration. Whatever angular velocity it has, is not changed. Simple. Other forces might or might not be present - the only important thing is if they cause a net torque.

But will the body rotating with constant angular velocity can have zero force

... the answer is yes, a body rotating (constant angular velocity or not) can easily have a net force acting on it, as long as that net force doesn't cause a torque (which it doesn't, if it pushed in the centre-of-mass e.g.).