A star of mass M = 2 x 10 30 kg is observed to have an angular speed of 0 = 7.3

Question

Explanation / Answer

Moment of Inertia of a uniform solid sphere, I = (2/5)(M*R^2)

In this case we have to apply conservation of angular momentum

Means –

I1*w1 = I2*w2

put the values –

[(2/5)(M*R1^2)]*w1 = [(2/5)(M*R2^2)]*w2

=> R1^2*w1 = R2^2*w2

given that –

R1 = 7.0 x 10^8 m, w1 = 7.3x10^-6 rad/s, R2 = 3.0X10^4 m, w2 = ?

So,

w2 = [(7.0 x 10^8 / 3.0X10^4)]^2*( 7.3x10^-6) = 3974.44 rad/s = 3.97x10^3 rad/s

So, the new angular speed of the star, w2 = 3.97x10^3 rad/s.

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