Samagra G.

asked • 11/07/16

momemt of inertia

We have to find moment of inertia of a semi circular disc whose axis of rotation is passing through the centre making an angle k with the diameter and lying in the plane of disc .

2 Answers By Expert Tutors

By:

Samagra G.

How is moment of inertia is preserved by symmetry . And how we get the new shape
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11/08/16

Samagra G.

Can you please tell me a start how to use polar coordinates .
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11/09/16

Steven W.

tutor
The way I looked at it was to define the perpendicular distance from the axis as "rsinθ."  And each little differential mass unit, dm, is just the (constant) mass density of the disc (which I will call μ) times the differential unit of area; which, in polar coordinates, is rdrdθ.  Then the integral becomes:
 
∫(rsinθ)2(μrdrdθ)
 
I integrated this in r from 0 to R, where R is the radius of the disc, and from -k to 180-k in θ.  I lost a factor of two in there, but the k dependence did, indeed, drop out, as Roman's elegant solution states.
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11/09/16

Samagra G.

Why the answer using this is coming the half of original answer .
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11/09/16

Steven W.

tutor
I would have to check to see where the factor of 2 comes from.  But the principle Roman expressed is absolutely correct, that there is no k dependence.
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11/09/16

Samagra G.

Yes that expression is correct
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11/09/16

Steven W.

tutor
Yes, actually, it should be MR2/4, because the full disk would be MR2/2.
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11/09/16

Samagra G.

Thanks a lot
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11/09/16

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