# A problem on rotational motion and angular momentum (small disc rotating on top of a larger disc)

vcsharp2003
And if the bodies in interest are rigid, a linear motion of the CoM implies the same linear motion for every point of the rigid bodies.
You mean the same translation motion for each point of the rigid body.

Delta2
vcsharp2003
It is always valid to represent a motion as a sum of motions, and it often helps to represent a rotation about a point other than the CoM as a rotation about the CoM plus a linear motion of the CoM.
I am assuming that the disks are in a horizontal position due to the mentioned vertical axis in problem statement. I am hoping that was also your assumption.

vcsharp2003
And if the bodies in interest are rigid, a linear motion of the CoM implies the same linear motion for every point of the rigid bodies.
So, when determining angular momentum about it's center axis, the translation motion part will not contribute to the angular momentum, only rotational part will contribute to angular momentum. Is that right?

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I am assuming that the disks are in a horizontal position due to the mentioned vertical axis in problem statement. I am hoping that was also your assumption.
If it is floating in space there is no vertical or horizontal. The reference to a vertical axis is strange anyway since it had not stated the disks were horizontal. I feel it was just a clumsy way of trying to say an axis normal to the plane of the disks.

vcsharp2003 and Delta2
vcsharp2003
If it is floating in space there is no vertical or horizontal. The reference to a vertical axis is strange anyway since it had not stated the disks were horizontal. I feel it was just a clumsy way of trying to say an axis normal to the plane of the disks.
But, what you said in post#27 and 29 wouldn't change even if the disks were horizontally aligned?

vcsharp2003
It is always valid to represent a motion as a sum of motions, and it often helps to represent a rotation about a point other than the CoM as a rotation about the CoM plus a linear motion of the CoM.
Based on the fact about translation motion plus rotational motion, I reached the following conclusion. The smaller disk is considered a point mass.

vcsharp2003
As previously noted (Post #12) the question is from this exam paper:

It wasn't too hard to find the official solutions. They are here:
Wow, you're a master in Google search. I spent many hours to search for original test paper and also it's solutions, but I couldn't get your results even after using your suggestion in an earlier post.
Very few people in today's world will have your skills for Google search.

Steve4Physics
vcsharp2003
If it is floating in space there is no vertical or horizontal. The reference to a vertical axis is strange anyway since it had not stated the disks were horizontal. I feel it was just a clumsy way of trying to say an axis normal to the plane of the disks.
Please see my final working based on your inputs in post #41. After @SteveForPhysics posted the solution link, I cross checked my answer with problem#13 in that solution sheet and it exactly matches. Wow, what an effort. This was after all a good problem and not an impossible problem.

haruspex and Lnewqban
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