Determining $L_{o}$: Finding Angular Momentum of System

[haruspex]

I was thinking that there is a fixed axis going through O', and another fixed axis going through O. And the larger disk is rotating about the O' axis. As the larger disk rotates, the O axis as well as O' axis remain fixed.

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]

If the large disk is initially set to rotate about O' then we can resolve that into a rotation about its centre plus a linear motion of the centre.

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?
If yes, then this is pretty advanced stuff for me.

I know that a rolling object on a horizontal surface without slippage, can have its motion resolved into a translational motion and a pure rotation about it's center as you have mentioned.

 

[haruspex]

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?

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.

 

[Delta2]

plus a linear motion of the CoM.

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.

 

[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.

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.

 

[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.

 

[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?

 

[haruspex]

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]

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.

 

[Steve4Physics]

As previously noted (Post #12) the question is from this exam paper:
https://www.fiitjeenorthwest.com/admin/upload/AITS-1819-OT-JEEA-PAPER-2_3-2-19.pdf

It wasn't too hard to find the official solutions. They are here:
https://fiitjeefaridabad.weebly.com/uploads/8/6/6/9/8669642/aits-1819-ot-jeea-paper-2-sol.pdf

 

[vcsharp2003]

As previously noted (Post #12) the question is from this exam paper:
https://www.fiitjeenorthwest.com/admin/upload/AITS-1819-OT-JEEA-PAPER-2_3-2-19.pdf

It wasn't too hard to find the official solutions. They are here:
https://fiitjeefaridabad.weebly.com/uploads/8/6/6/9/8669642/aits-1819-ot-jeea-paper-2-sol.pdf

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.

 

[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.

 

[Steve4Physics]

Very few people will have your skills for Google search.

I Googled:
jee advanced 2019 paper 2 "03-02-2019" solutions

Not that clever, though I had to put the date in quotes as a refinement. The answer was the 4th match. Try it for yourself.

 

[vcsharp2003]

I Googled:
jee advanced 2019 paper 2 "03-02-2019" solutions

Not that clever, though I had to put the date in quotes as a refinement. The answer was the 4th match. Try it for yourself.

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.