bluesky Posted May 4, 2007 Report Share Posted May 4, 2007 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. Quote Link to comment Share on other sites More sharing options...
Qfwfq Posted May 8, 2007 Report Share Posted May 8, 2007 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. Quote Link to comment Share on other sites More sharing options...
ronthepon Posted May 9, 2007 Report Share Posted May 9, 2007 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) Quote Link to comment Share on other sites More sharing options...
Qfwfq Posted May 9, 2007 Report Share Posted May 9, 2007 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.... :) Quote Link to comment Share on other sites More sharing options...
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