The moment about points in a rigid body

[gladius999]

If a rigid body has a net moment e.g. rotating clockwise at 2Nm moment about the centre of mass, does every point on the body have 2Nm moment? Or just the point at the centre of mass have a net moment?

Thanks

 

[tiny-tim]

hi gladius999!

i haven't heard of "net moment" of a body …

Nm is Newton-metres ie force times distance, so that's torque …

torque = Iα just as force = ma, but we don't talk of the "net force" of a body

 

[gladius999]

hi tiny-tim,

I think i meant resultant moment then haha. An object subject to force that is not on its centre of mass will experience a moment would it not? Is that moment only around the centre of mass or does it apply to every point on the body?

 

[Studiot]

Any system of forces acting on a rigid body can be reduced to a net force or resultant force plus a net couple or resultant couple.

Either may independently be zero.

So yes you can have zero net resultant force but a real valued resultant couple.

The couple has the same turning effect on all parts of the body.

This is true in 2 dimensions or 3 dimensions and is known as Poinsot's theorem.

 

[Tosh5457]

If a rigid body has a net moment e.g. rotating clockwise at 2Nm moment about the centre of mass, does every point on the body have 2Nm moment?

With torque = I*angular_aceleration = m*angular_aceleration*r^2 for a particle, for the same force, if you increase the distance to the rotation axis the torque also increases, so it's not the same for every particle on the body.
When we say a rigid body has a torque of 2 Nm, it means the total sum of the torque of each particle is 2 Nm, it doesn't mean it's being exerted 2 Nm of torque on each particle.

On the center of mass, if it coincides with the rotation axis, r = 0, so torque = 0.