When some stars use up their fuel, they undergo a catastrophic explosion called

Question

When some stars use up their fuel, they undergo a catastrophic explosion called a supernova. This explosion blows much or all of the star's mass outward, in the form of a rapidly expanding spherical shell. As a simple model of the supernova process, assume that the star is a solid sphere of radius R that is initially rotating at 2.0 revolutions per day. After the star explodes, find the angular velocity, in revolutions per day, of the expanding supernova shell when its radius is 4.0R. Assume that all of the star's original mass is contained in the shell.

Explanation / Answer

by conservation of momentum

I1*w1 = I2*w2
w2/w1 = I1/I2
solid sphere of radius 'R' the moment of inertia (I1) about an axis is 2/5*m*R^2

For a hollow sphere of radius 4*R, I2 is 2/3*m*(4*R)^2 = 32/3*m*R^2

w2/w1 = (2/5)/(32/3) = 3/80
w2 = 3/80*w1 = 3/80*2 = 0.075 rev/day

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