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![[Post New]](/templates/default/images/icon_minipost_new.gif) 9 May 2007 13:34:43 IST
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A uniform circular disc of mass m and radius r placed on a smooth horizontal surface with its plane parallel to the horizontal surface is rotating about its axis with angular speed W and also translating with speed 2WR. The disc is suddenly hinged at the top point. Find final angular velocity of the disc.
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9 May 2007 13:53:08 IST
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is it (root3)W?
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9 May 2007 14:10:53 IST
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no the ans is 5W/3
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9 May 2007 15:59:02 IST
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what do u mean by suddenly hinged?
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9 May 2007 16:18:19 IST
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in any time od its motion you get hold of the topmost point, the disc will now only rotate and not translate.
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9 May 2007 19:08:29 IST
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okay the solution is.
the angular mom. before the hinge. is mr^2\2W and linear is m2wr*r as it is alwais mvr.
now after it is hinged the translational motion has stopped and it can only rotate with ang. vel. w' but inertia has to be taken about the hinged poiint therefore mr^2\2 +mr^2=3mr^2\2(paraalel axis theorem)
now initial momen=final
mr^2W+2mr^2W*2=3mr^2w'
hence w'=5W\3
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10 May 2007 09:20:01 IST
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hey joy just conserve initial & final angular momentum about the topmost point see initial angular momentum about topmost point is (mR^2W)/2 + m(2RW)R final angular momentum about topmost point is 3/2mR^2W' therefore by conservation of angular momentum 5/2mR^2W = 3/2mR^2W' therefore W' = (5W)/3
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10 May 2007 11:02:28 IST
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This might be a dumb question.... but... why can't we conserve energy?
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10 May 2007 21:27:29 IST
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anyone?
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11 May 2007 05:57:02 IST
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simple..........since its not told that no energy is required to hinge the disc we will not be able to account that energy considerations
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