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.
rev/day

Explanation / Answer

Assuming angular momentum is the conserved quantity,
the value of (moment of inertia) times (angular speed)
will be the same after the explosion as before.

The moment of inertia of a solid sphere is (2/5)mr^2,
while that of a hollow spherical shell is (2/3) mr^2.
So the moment of inertia in this problem increases by a factor of
(5/3)(4)^2 = 26.66
Therefore, the rotation rate decreases by this same factor, and ends up as
(2/26.66) rev/day = 0.075 rev/day [or maybe they want it rounded to 0.075 rev/day].

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