Deriving relation between angular momentum reduction by torque

[caspernorth]

Friction causes a torque that opposes angular momentum. It gets reduced. how can we derive a relation connecting these. friction starts with maximum and becomes zero. angular velocity and its corresponding momentum decreases maximum in the beginning and increases towards the end. the radial vector of friction and center of mass of disk changes from r1 to r2.

 

[Doc Al]

It's a bit hard to understand what you're looking for. Say you have a wheel spinning (I) and the only force acting on it is friction acting to slow it down. The angular acceleration due to the frictional torque is given by Torque = I*alpha.

 

[caspernorth]

I knew it would be hard, sorry. Let me phrase it in a simple way.
There is a disc with a hole (I recently posted here asking for its moment of inertia). It is spinning about an axis passing through its own diameter. Due to the shift in point of contact and center of mass the disc scratches the ground and this friction creates a torque opposing the angular frequency. (angular momentum in the direction). this opposing is happening when the center of mass is on the bottom. This friction will also bring the center of mass upwards (like a tippie top) till the line of center of mass co-incides with the sliding point.
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Now friction decreases, angular frequency goes back to normal and meanwhile a change in radial vector also occured. (from center of mass to diameter minus center of mass).

how can all these changes expressed in an equation.

 

[caspernorth]

W = integral of (torque x dθ) = Iω^2 / 2
Considering change in torque is difficult i guess. since Radial vector changes and the dθ is infact a tilt to backwards... so I guess we need a much complicated differential equation, isn't that so?
Change in torque is rather uncommon in such cases right? is this a case of change in acceleration-jerking. I've never seen an equation including jerking.

 

[Doc Al]

This reminds me of (and I suspect that it's equivalent to) the infamous "tippy top" toy. The analysis is non-trivial.

https://www.youtube.com/watch?v=AyAgeUneFds

 

[caspernorth]

This reminds me of (and I suspect that it's equivalent to) the infamous "tippy top" toy. The analysis is non-trivial.

https://www.youtube.com/watch?v=AyAgeUneFds

But, after going through the tippie top's theory
:http://ckw.phys.ncku.edu.tw/public/...ons/Tippy Top/Gray-Nickel_AJP68-821(2000).pdf

I think a similar case can be applied here, except that the moment of inertia in 3 axes would have to be modified to suit the disk. what do you think?

 

[caspernorth]

By the way, I need a help in doing a project based on this(the disc's strange behaviour and similar objects like tippy-top). How can i include a sample calculation that shows how long the disc will stay in its stable position, how much time will it take to flip the hole position. How can i make the topic presentable.
any ideas on this, please help.