1, A star with a mass of 1.25 × 1031 kg and a radius of 3.45 × 105 km is initial
ID: 778779 • Letter: 1
Question
1, A star with a mass of 1.25 × 1031 kg and a radius of 3.45 × 105 km is initially rotating on its axis with a period of 24.0 days. The star collapses and becomes a neutron star with a radius of 12.5 km, retaining all of its original mass. Assume the star is a uniform solid sphere before and after the collapse, with a moment of inertia given by (2/5)MR2. What is the period of rotation after collapse? Give your answer in seconds. Hints: solve this problem by using conservation of angular momentum.Explanation / Answer
We know by law of conservation of angular momentum
I1w1 = I2w2 where I is moment of inertia and w is rotational speed
w = 2*pi/T
w1 = 2*3.14/(24*24*60*60) rad
Therefore
I1w1 = I2w2
(2/5*M*R1^2*2*PI)/(24*24*3600) = (2/5*M*R2^2*2*pi)/(T)
T = 12.5e3*24*24*3600/(3.45e8) = 75.13 seconds
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