torque on a body without any supporting point

Question

Suppose there is a rigid body in space and one single force is acting on it and the force does not pass through the center of mass. I would like to ask why the torque on a body is always the force times perpendicular distance to the center of mass if there is no supporting point on that body? What's the principle behind that?

The question has been answered here Why is moment dependent on the distance from the point of rotation to the force also. — John Alexiou, Aug 12 '14 at 22:33

score 1 · Answer 1 · answered Jun 05 '14 at 04:52

1

There is no such principal

We can find the torque about any axis whatsoever we find suitable.

But while facing problems on classical mechanics, there is a singular advantage of finding out the torque through the COM. That is we dont have to account for the torque caused by the body's own weight.

answered Jun 05 '14 at 04:52

Normie

1,456

What if the object is in free space and there is only one force? If we take moment about different axis we get different torques, but there can only be one result. Why the torque about COM is the correct one? – Kelvin S Jun 05 '14 at 06:07
Well there is no right one. you can take torques based on any axis of your choice and proceed on your problem – Normie Jun 05 '14 at 06:11
the different results are expected and in not any way wrong – Normie Jun 05 '14 at 06:12
Will different angular acceleration be obtain if we take moment at different point? – Kelvin S Jun 05 '14 at 06:34
yes naturally they would also be different – Normie Jun 05 '14 at 09:20
but the rigid body can only have one resultant motion, if different angular acceleration be obtain how do we know which one will be the actually acceleration? – Kelvin S Jun 05 '14 at 09:32

score 0 · Answer 2 · answered Jun 06 '14 at 02:05

For rigid body in space and one single force is acting on it. If we calculate the moment at different point we obtain different torque. But the body can only have one resultant motion, if different angular acceleration be obtain how do we know which one will be the actual acceleration?

score 0 · Answer 3 · edited Apr 13 '17 at 12:39

There is a principle which states that for a rigid body:

The net loading can be represented as a 3D line, a magnitude and a pitch. This is the loading screw or wrench.
The not motion can be represented as a 3D line, a magnitude and a pitch. This is the motion screw or twist.

For both cases the parallel separation of the point of interest from the screw line does not affect the results. This is because a 3D line extends to infinity both ways and due to cylindrical symmetry the resulting vector field is a function of perpendicular distance only.

See https://physics.stackexchange.com/a/80552/392 for the answer to a similar question.

torque on a body without any supporting point

3 Answers3