Physics GRE Discussion Forums

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 ?

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

ali8 wrote:So there's a missing/additional factor of 2. Could you please tell me what I am missing ?

$$\lambda = \frac{M}{2d}$$

@ 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...