Angular momentum: disk with point mass on the edge

AI Thread Summary
The discussion centers on calculating the instantaneous angular momentum of a disk with an additional point mass on its edge, which is both rotating and translating. The total angular momentum of the system can be determined by summing the angular momentum of the disk and the point mass. However, the moments of inertia must be adjusted to account for the shift in the center of mass caused by the point mass. It is clarified that the moment of inertia of the disk changes depending on the axis of rotation, and the contribution from the point mass must be included in the calculations. The conversation emphasizes the importance of understanding how the addition of the point mass affects the overall dynamics of the system.
willywilly
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Hi all,

I'm treating a problem concerning a disk containing an additional point mass on the edge. The disk is moving (rotating and translating) relative to another fixed point, meanwhile it's spinning about its axes of symmetry.
I'd like to determine the instantaneous angular momentum about the disk center and the resulting instantaneous moment the system (point mass+disk) exerts on the disk center.

Is the total angular momentum equal to the angular momentum of the point mass + the angular momentum of the disk?
Is it allowed to consider the moments of inertia about the disk center unchanged when an additional point mass is added, neglecting the latter?

Thanks in advance.

Regards,
WillyWilly
 
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you can assume the conservation of angular momentum

Not clear where the point of rotation is - is it fixed at the centre of the disk?

In other words a shift in centre of gravity when the point mass is added on the disk
 
The rotation is about the center of gravity of the disk, called G, containing no point mass.
 
Total angular momentum is indeed a simple sum of angular momenta of the constituents, as are the moments of inertia, but it is not that simple in your case because the moment of inertia of the disk (without considering the point mass) is different about different axes, and the presence of the point mass fixed to the disk has shiften the centre of mass outwards from the centre.edit- oh I misread, if the disk is still spinning about its centre, then the total moment of inertial is that of the disk plus the mr^2 from the point.
 

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