Answer to Question #111070 in Mechanics | Relativity for Balogun Raheem

Question #111070
suppose a uniform spherical star of mass M and radius R collapses to a uniform sphere of radius 10^-5 .If the original star had a rotation rate of 1 rev each 25 days(as does the sun) ,what will be the rotation rate of the resulting object
1
Expert's answer
2020-04-21T19:19:20-0400

As per the question,

Mass of the spherical star=M

Radius of the spherical star= R

Radius of the other star=105R=10^{-5}R

rotational speed of the first starω1=1/25rev/day\omega_1= 1/25 rev/day

rotational speed of the second star ω2=?\omega_2=?

Now, applying the conservation of angular momentum,

I1ω1=I2ω2I_1\omega_1=I_2\omega_2

ω2=I1ω1I2=101025=4×108rev/day\Rightarrow \omega_2=\dfrac{I_1\omega_1}{I_2}=\dfrac{10^{10}}{25}=4\times 10^8 rev/day

ω2=4.6×103rev/sec\omega_2=4.6\times 10^3 rev/sec


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