Rotation problem

[bluesky]

A rotating sphere contract slowly due to internal forces to (1/n)th of its original radius.What happens to its angular velocity.Show that increase in its energy equals the work done during its contraction.

 

(2/5)MR^2*w_1=(2/5)M(R/n)^2*w_2

 

From this we should find the change in w.

Regarding the workdone: Please help me to start with.

[Qfwfq]

Well, what you have here is:

 

[math]\frac25 MR^2 w_1=\frac25 M(\frac{R}{n})^2 w_2[/math]

 

Can you see how the moment of inertia, [math]\norm\frac25 MR^2[/math], changes? Write the new one in terms of n and the old one and you should be able to get it.

[ronthepon]

Okay, using that we could go on to find the change in energy of the spinning sphere.

 

What I can't figure is how to analyse the work done in contracting the spinning sphere. (Other than talk about the law of conservation of energy)

[Qfwfq]

Obviously the work must be equal to the change in kinetic energy, therefore the integral of centrifugal forces in dr must equal the difference.

 

Perhaps your difficulty is due to asking about potential energy. Yep, that requires a spot of careful thinking.... :)