The discussion revolves around calculating the moment of inertia, particularly for a hollow disk containing a small metal ball. Participants explore the implications of mass distribution on inertia calculations and the application of relevant theorems.
The discussion is active, with participants providing guidance on calculating moments of inertia separately and referencing the need for clarity on the specific shapes involved. There is acknowledgment of the complexity introduced by the internal rim and the necessity of understanding different objects' inertia properties.
Some participants note that they have not yet learned about the parallel axis theorem, which may limit their approach to the problem. Additionally, the presence of an internal rim affecting the ball's position introduces further complexity to the calculations.
goomer said:I know that for for solid disks, the inertia is equal to (1/2)mr^2 and for hoops is just mr^2. This only works for if the mass is evenly distributed around though. So what about when the mass isn't equally distributed? How would you solve for the moment of inertia of a hollow disk if a small metal ball inside of it?
gneill said:You could determine the moment of inertia of the objects separately and add them. The parallel axis theorem may be of use if the object's individual moments of inertia are not co-aligned on the axis of rotation.
goomer said:We haven't learned about the parallel axis theorem yet, so I don't think I need to use that.
I forgot to mention that there is a rim inside the disk that keeps the ball at a constant distance away from the radius. Sorry! Would you still calculate the moments of inertia separately? How do you do that?