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 a 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 2.9 revolutions per day. After the star explodes, find the angular velocity, in revolutions per day, of the expanding supernova shell when its radius is 3.3R. Assume that all of the star's original mass is contained in the shell.

Explanation / Answer

initial I = (2/5)MR² solid sphere
final I = (2/3)M(3.3R)² = 7.26MR² shell

Conserve angular momentum: initial I* = final I*
0.4MR² * 2.9rev/day = 7.26MR² * MR² cancel

= 2.9rev/day + 0.4 / 7.26 = 0.4545 rev/day

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