Question

The mass of a star is 1.41·1031 kg and its angular velocity is 1.60E-7 rad/s. Find...

The mass of a star is 1.41·1031 kg and its angular velocity is 1.60E-7 rad/s. Find its new angular velocity if the diameter suddenly shrinks to 0.51 times its present size. Assume a uniform mass distribution before and after. Icm for a solid sphere of uniform density is 2/5 mr2.

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Answer #1

Hi buddy!

Let me try and help you to solve the above question!

Let us keep
I1, I2 be the original and changed moments of inertia respectively.
w1 and w2 are the original and changed angular velocities,
r1, r2 be the the original and changed radii,
also m is the mass.

Equating angular momentum before and after shrinkage:
I1 w1 = I2 w2

(2 / 5)mr1^2 w1 = (2 / 5)mr2^2 w2

w2 = r1^2 w1 / r2^2

Putting r2 = 0.49 r1:
w2 = w1 / 0.49^2

I got the answer around

6.25 * 10^(- 7) rad / s.

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