The moment about points in a rigid body

In summary, a rigid body can have a net moment or torque, which is the sum of all the individual torques of the particles in the body. This moment or torque can be zero if the net force is zero, but there can still be a nonzero net couple or resultant couple. This couple has the same effect on all points of the body and is known as Poinsot's theorem. The torque on a rigid body is not the same for every point on the body, as it depends on the distance from the rotation axis. A body with a torque of 2 Nm means the total sum of the torques of its particles is 2 Nm, not that each particle is experiencing a torque of 2 Nm.
  • #1
gladius999
60
0
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
 
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  • #2
hi gladius999! :smile:

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 :confused:
 
  • #3
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?
 
  • #4
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.
 
  • #5
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.
 

What is a moment about a point in a rigid body?

A moment about a point in a rigid body is a measure of the tendency of a force to cause rotation around that point. It takes into account both the magnitude and direction of the force, as well as the distance from the point to the line of action of the force.

How is the moment about a point calculated?

The moment about a point is calculated by multiplying the magnitude of the force by the perpendicular distance from the point to the line of action of the force. This distance is also known as the lever arm.

What is the difference between a positive and negative moment?

A positive moment indicates a counterclockwise rotation, while a negative moment indicates a clockwise rotation. This is determined by the direction of the force and the direction of the lever arm.

What is the unit of measurement for moment about a point?

The unit of measurement for moment about a point is newton-meters (Nm) or pound-feet (lb-ft) in the SI and US customary systems, respectively. This unit represents the product of force and distance.

How is the moment about a point used in real-world applications?

The moment about a point is used in engineering and physics to analyze the stability and equilibrium of structures and objects. It is also used in designing structures and machines to ensure they can withstand external forces without collapsing or breaking.

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