The discussion centers on determining the angular momentum ($L_{o}$) of a system comprising two disks, one larger and one smaller, with specific angular velocities. The angular momentum is calculated using the formula $L_{o} = I_{so} ~ \omega_{1} + I_{lo} ~ \omega_{1}$, where $I_{so}$ and $I_{lo}$ represent the moments of inertia of the smaller and larger disks, respectively. The relationship between angular velocities $\omega_{1}$ and $\omega_{0}$ is established as $\omega_{1} = \frac{\omega_{0}}{2}$. The discussion highlights ambiguities in the problem setup, particularly regarding the mounting of the disks and the absence of friction, which affects torque considerations.
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I thought we agreed in posts #25 and #27 that there is no axle fixed in space. The two disk system is floating in space. All that is 'fixed' is that there is an axle mounted on the large disk, and the small disk rotates freely about that. And as I noted in post #29, this means the rotation of the smaller disk is irrelevant and we can replace it with a point mass fixed to the larger disk at O'.vcsharp2003 said:
Is this fact always applicable when a disk rotates about a vertical axis perpendicular to the disk passing through a point other than it's center?haruspex said:
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.vcsharp2003 said:
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.haruspex said:
Ok, that's a very powerful truth. I was used to thinking in these terms only for a rolling object with no slippage on a horizontal surface since that's the scenario textbooks normally explain.haruspex said:
You mean the same translation motion for each point of the rigid body.Delta2 said:
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.haruspex said:
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?Delta2 said:
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 said:
But, what you said in post#27 and 29 wouldn't change even if the disks were horizontally aligned?haruspex said:
Based on the fact about translation motion plus rotational motion, I reached the following conclusion. The smaller disk is considered a point mass.haruspex said:
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.Steve4Physics said:
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 said:
I Googled:vcsharp2003 said:
For some reason, I'm not getting the 4th listing as the match. I'll look more into this. I'm not getting anything like an answer sheet, but I'll keep searching.Steve4Physics said: