# Torque of a force passing through AOR

I have a very basic conceptual doubt about torque, please pardon me. Suppose, we have a circle and a Normal reaction is passing through it's centre, also suppose the axis of rotation(AOR) is passing through the centre and perpendicular to its plane. As the normal reaction is passing through the AOR, its torque will be zero(as moment arm is zero. Is it?) But if we resolve the normal reaction into two components(not passing through AOR will they also have zero torque about the same AOR? How it can be in equilibrium, as Torque of Normal reaction is zero?(in picture) Here is an example figure

• What do you mean, when saying normal reaction passing through center. It would be great if you support your problem with a figure, if possible. – Abhinav Dhawan Oct 31 '17 at 12:51

## 1 Answer

As the normal reaction is passing through the AOR, its torque will be zero(as moment arm is zero. Is it?)

Correct. The torque relative to the center will be zero.

But if we resolve the normal reaction into two components(not passing through AOR will they also have zero torque about the same AOR? How it can be in equilibrium, as Torque of Normal reaction is zero?(in picture)

Yes. For any given arrangement, simply do the calculation to find this.

Given a point on the circumference, and a vector that points to the center, resolve the vector into two component vectors. Then calculate the torque for each about the center and add the torques. You will find that they sum to zero. So there is no net torque about the center from that specific force.