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A uniform, spherical cloud of interstellar gas has mass 2.0×1030 kg and radius 1.2×1013 m ,...

A uniform, spherical cloud of interstellar gas has mass 2.0×1030 kg and radius 1.2×1013 m , and is rotating with period 1.3×106 years. If the cloud collapses to form a star 6.9×108 m in radius, what will be the star's rotation period?

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Answer #1

moment of inertia of sphere

I=(2/5)mr2

By Conservation of angular momentum

I1W1 = I2W2

(2/5)mr12 (2pi/T1)=(2/5)mr22 (2pi/T2)

T2=T1(r2/r1)2

T22 =(6.9*108/1.2*1013)2 (1.3*106)

T2=4.3*10-3 years

or in days

T=4.3*10-3*365=1.5688 days

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