GR9277 #82

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ali8
Posts: 103
Joined: Sat Aug 29, 2009 8:20 am

GR9277 #82

Post by ali8 » Wed Jul 13, 2011 4:03 pm

OK so this is about Moment of Inertia

http://grephysics.net/ans/9277/82

The correct answer is I=(1/3)Md^2

But let's analyze it as follows:

$$I=\int r^2\,dm=\lambda \int^d_{-d} r^2\,dr=\dfrac{\lambda}{3} (d^3+d^3)$$

So finally we have:

$$I=\dfrac{2 \lambda d^3}{3}=\dfrac{2 M d^2}{3}$$

So there's a missing/additional factor of 2. Could you please tell me what I am missing ?

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HappyQuark
Posts: 762
Joined: Thu Apr 16, 2009 2:08 am

Re: GR9277 #82

Post by HappyQuark » Wed Jul 13, 2011 4:24 pm

ali8 wrote:OK so this is about Moment of Inertia

http://grephysics.net/ans/9277/82

The correct answer is I=(1/3)Md^2

But let's analyze it as follows:

$$I=\int r^2\,dm=\lambda \int^d_{-d} r^2\,dr=\dfrac{\lambda}{3} (d^3+d^3)$$

So finally we have:

$$I=\dfrac{2 \lambda d^3}{3}=\dfrac{2 M d^2}{3}$$

So there's a missing/additional factor of 2. Could you please tell me what I am missing ?
In Yosun's original problem, she accidentally put an extra factor of 2 in the denominator of the answer that is supposed to be the correct one. Look at the original question from the booklet and you'll see what I mean.

http://physicsgrad.com/pgre/9277-82

physicsworks
Posts: 80
Joined: Tue Oct 12, 2010 8:00 am

Re: GR9277 #82

Post by physicsworks » Wed Jul 13, 2011 4:34 pm

ali8 wrote:So there's a missing/additional factor of 2. Could you please tell me what I am missing ?
$$\lambda = \frac{M}{2d}$$

ali8
Posts: 103
Joined: Sat Aug 29, 2009 8:20 am

Re: GR9277 #82

Post by ali8 » Thu Jul 14, 2011 3:20 am

@ HappyQuark: Thanks, but anyway my problem is only with Moment of Inertia regardless
of the angular frequency (i.e. the final answer).

@ physicsworks: Oh you are right, that was the problem!!

Thanks everybody, I guess on need to be super-concenterating in the real PGRE...



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