Solving a Complex Rotational Dynamics Problem

[x2008kwa]

Hi all,

I've got a question that I'm stuck on.

Three disks are spinning independently on the same axle without friction. Their respective rotational inertias and angular speeds are I,w (clockwise); 2I,3w (counterclockwise); and 4I,w/2 (clockwise). The disks then slide together and stick together, forming one piece with a single angular velocity. What will be the direction and the rate of rotation of the single piece?
Express your answer in terms of one or both of the variables and and appropriate constants. Use a minus sign for clockwise rotation.


I haven't really made progress on this question. My prof is abosolutely useless (it's his first year at my university and most likely his last judging by all of the complaints). So basically I haven't been taught how to approach this problem. I've read the texbook and can't figure out how this problem can be solved.
Not necessarly just looking for the answer to the problem, but how to approach it.
Any help is greatly appreciated.

 

[LowlyPion]

Welcome to PF.

What does your book say about the conservation of angular momentum? Does it by any chance indicate that in a closed system that Angular Momentum remains constant?

Isn't that all you have to know?

 

[x2008kwa]

Thank you very much for your response.

Yes, I do know that angular momentum should be conserved... and that L = I x w...

Therefore I know that the angular momentum after the discs combine must be equal to the sum of all of the angular momentums of the individual discs... But I'm not sure how to go about combining these and obtaining the final angular speed. Any hints on how this is done?

 

[turin]

Since all three disks are on the same axis, you don't need to worry about different directions in 3-D, but you do need to worry about clockwise vs counterclockwise. These will get opposite signs, and the problems tells you which one to make negative. Then, you use your equation for the three individual L's, and add them together with the appropriate signs to get the resulting L. Finally, to obtain the resulting w, you use your equation again to solve for it, but you need to know the resulting I. Since this is all on the same axis, the I's just sum, all with the same sign (because, like mass, I cannot be negative).

 

[LowlyPion]

Thank you very much for your response.

Yes, I do know that angular momentum should be conserved... and that L = I x w...

Therefore I know that the angular momentum after the discs combine must be equal to the sum of all of the angular momentums of the individual discs... But I'm not sure how to go about combining these and obtaining the final angular speed. Any hints on how this is done?

Then figure simply that the sum of the L (using the sign convention required by the problem) divided by the total I will be your final ω .

 

[x2008kwa]

Thanks a ton for the help guys. Makes complete sense...
Got the answer correct now. Much appreciated.