posted by Cat on .
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 1.5 revolutions per day. After the star explodes, find the angular velocity, in revolutions per day, of the expanding supernova shell when its radius is 3.7R. Assume that all of the star's original mass is contained in the shell.
Angular momentum is conserved. That means, in this case,
I1*w1 = I2*w2
where w is the angular velocity and i is the moment of inertia.
The moment of inertia of a solid sphere of uniform density with mass M and radius R1 is
I1 = (2/5)M*R1^2
The moment of inertia of a thin spherical shell of radius R2 is
I2 = (2/3)M*R2^2
The angular velocity w decreases by the ration factor
w2/w1 = I1/I2 = [(2/5)/(2/3)](R1/R2)^2
= (3/5)*(1/3.7)^2 = 0.044
The supernova shell will require 1.5/0.044 = 34 days for a single rotation.
conservation of momentum
Io wi = If wf
Io for a sphere...mass m, radius R
If for a sphericalshell, massm, radisu 3R
Why is R1 equal to 1?