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

AI Thread Summary
The discussion centers on calculating torque around an arbitrary point on a rotating disc with a force acting on its rim. When considering torque about point O, an additional force must be included to balance the applied force F, especially since the disc is only engaged in rotational motion. The rotation rates of any points on the rigid body are identical, meaning that angular accelerations are also the same. It is confirmed that point A is fixed to the rotating body and that the reference frame is non-rotating. Understanding these dynamics is crucial for accurately determining torque and angular acceleration in this context.
John Milton
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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?

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There must be an additional force about the point O if the disk is not also accelerating linearly.
 
Apologies, suppose there is a frictionless rod through the point O, so the disc is only engaged in rotational motion.
 
John Milton said:
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.
 
John Milton said:
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?
 
jbriggs444 said:
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
 
John Milton said:
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.
 
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