IIT JEE , AIEEE Forum - Physics , Thermal Physics

abhaysrinivas3012

the moment of inertia of a body is I.The coefficient of linear expansion of the material isA.Fractional change in moment of inertia whe there is fractional change in temprature is

iitkgp_bipin

Moment of inertia, I = mr²
where r is the radius of gyration.

For any temperature change

T.

So, new radius of gyration = r(1 + A

T)

I' = m{r(1 + A

T)}²

I' = mr²(1 + A

T)² = I(1 + A

T)²

When 1 >> A

T

I' is approximately equal to I(1+2A

T)

so fractional change for fractional change in temperature is 2A

T.

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