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GR9677 #21
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Problem
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This problem is still being typed. |
Mechanics }Moment of Inertia
To solve this problem, one should remember the parallel axis equation to calculate the moment of inertia about one end of the hoop:
 ,
where  is the distance from the pivot point to the center of mass, which in this problem, is just equal to  . (In the last equality, note that the moment of inertia of a hoop of radius R and mass m about its center of mass is just  .)
The problem gives the period of a physical pendulum as }) . Thus, plugging in the above result for the moment of inertia, one has, }=2\pi \sqrt{2R/(g)} \approx 2*3\sqrt{2*0.2/(10)}= 12/10=1.2s) , which is closest to choice (C). (Since  was rounded to 3, the period should be slightly longer than 1.2s.)
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Comments |
Goddar
2009-10-08 10:39:29 | as far as i can tell, this result is correct only for an oscillation along the vertical axis; if we take the oscillation to be about the horizontal axis (as if a bird were swinging on the hoop), it seems after a quick calculation that (B) is closer to the answer, since the moment of inertia is not the same (perpendicular axis theorem)...
correct me if i'm wrong
fearmyplectrum
2009-10-09 16:05:14 |
I think that's why they specify the nail is on a barn wall... the wall restricts the hoop from oscillating in the horizontal axis.
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|  | furlong
2009-08-12 19:50:59 | How come you cant just treat the hoop like a point mass at the center of the hoop oscillating from the nail at a distance R?
dstahlke
2009-10-08 20:42:00 |
Because the hoop has a nonzero moment of intertia, and a point doesn't. When the thing is swinging it has extra angular momentum due to the moment of intertia of the hoop.
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| | petr1243
2008-04-10 17:11:33 | no need for parallel axis theorem, just know I for the hoop and you are fine, then use d = 2r.
nobel
2008-11-03 20:43:56 |
hatt
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carle257
2010-04-04 19:46:02 |
What motivation do you have for using d=2r? It also doesn't work out. You must have multiplied by d instead of divided because your answer would yeild ~.6 using d=2R. The moment of inertia about about the edge of the hoop is 2mR^2 as yosun correctly calculated, and that is the correct way to go about the problem.
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