A star rotates once every 100 hours and then collapses to 1/10 of its original
radius. What is the new period of rotation?
radius. What is the new period of rotation?
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this is a problem in conservation of momentum
assuming there is no loss of mass, we can write
I1 w1 = I2 w2
I, w are moment of inertia and angular velocity
1, 2 refer to values before, after collapse
the moment of inertia of sphere varies as 2/5 MR^2, so if the radius becomes 1/10 of the original value, the moment of inertia decreases by a factor of 1/100
therefore the angular velocity increases by a factor of 100 to maintain the same value of angular momentum
this means the star rotates 100 times faster, and its new period will then be 1 hour
assuming there is no loss of mass, we can write
I1 w1 = I2 w2
I, w are moment of inertia and angular velocity
1, 2 refer to values before, after collapse
the moment of inertia of sphere varies as 2/5 MR^2, so if the radius becomes 1/10 of the original value, the moment of inertia decreases by a factor of 1/100
therefore the angular velocity increases by a factor of 100 to maintain the same value of angular momentum
this means the star rotates 100 times faster, and its new period will then be 1 hour