Writing an equation for torque around an arbitrary point on a body

[John Milton]

TL;DR

Writing an equation of torque around arbitrary point

Suppose there is a disc rotating around axis through its centre, with force F acting on the rim. The equation of torque is simple, however, what happens if it is written about an arbitrary point on the rim? How can the angular acceleration about that point be understood? Do I have to transition to its frame of reference?

 

[PeroK]

There must be an additional force about the point O if the disk is not also accelerating linearly.

 

[John Milton]

Apologies, suppose there is a frictionless rod through the point O, so the disc is only engaged in rotational motion.

 

[PeroK]

Apologies, suppose there is a frictionless rod through the point O, so the disc is only engaged in rotational motion.

Frictionless rod or not, there is a force at O.

 

[jbriggs444]

How can the angular acceleration about that point be understood?

For a rigid body in a plane, the rotation rate of any point about any other point is identical. The orientations of any lines you draw on the body will change in lock step.

If the rotation rates are the same, the angular accelerations are the same.

I assume that point A is fixed to the rotating body? And that we are referencing rotation rates against a non-rotating background?

 

[John Milton]

For a rigid body in a plane, the rotation rate of any point about any other point is identical. The orientations of any lines you draw on the body will change in lock step.

If the rotation rates are the same, the angular accelerations are the same.

I assume that point A is fixed to the rotating body? And that we are referencing rotation rates against a non-rotating background?

Thank you for the reply. Yes, the point is fixed, and the background is not rotating

 

[A.T.]

Thank you for the reply. Yes, the point is fixed, and the background is not rotating

As @PeroK noted, you need to include the foce at O, which balances F and also contributes to the torque around A.