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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 $2\mathrm{.}8$ revolutions per day. After the star explodes, find the angular velocity, in revolutions per day, of the expanding supernova shell when its radius is $4\mathrm{.}0$ R$.$ Assume that all of the star's original mass is contained in the shell.

Before: solid sphere

After: expanding spherical shell

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