Arbitrary value of the moment of a force

[fog37]

Hello,
It is well know that the moment of a force ##F## depends on:
a) the force magnitude ##|F|##
b) the choice of the moment reference point ##P##
c) the distance (lever arm) from the point ##P## to the point of application of the force ##Q##.

That said, an object with a single force applied to it will experience a moment which will vary in magnitude and sign with difference choices of the moment reference point ##P##. However, physically, the object will move in one specific and unique way under that same force (rotation+translation). How do different values of the moment ##M## produce the same physical situation?

Maybe all angular quantities, like angle, angular velocity, angular acceleration, moment of inertia, rotational kinetic energy, etc. must be referred to that specific and arbitrarily chosen point ##P##?

In general, we refer vectorial quantities (position, velocity, acceleration) to the origin ##O## of the triad of Cartesian axes...

 

[jbriggs444]

Hello,
It is well know that the moment of a force ##F## depends on:
a) the force magnitude ##|F|##
b) the choice of the moment reference point ##P##
c) the distance (lever arm) from the point ##P## to the point of application of the force ##Q##.

That said, an object with a single force applied to it will experience a moment which will vary in magnitude and sign with difference choices of the moment reference point ##P##. However, physically, the object will move in one specific and unique way under that same force (rotation+translation). How do different values of the moment ##M## produce the same physical situation?

The same linear momentum counts as a different amount of angular momentum depending on the location of the reference point.
The same linear force counts a a different amount of torque depending on the location of the reference point.

The two effects match so that no matter where you choose to put the reference point, the rate of change in angular momentum will match the applied torque. Moving the reference point simply gives a different set of coordinates to describe the same physical reality.