A star (such as the sun) rotates about its axis every 25 days. The star has a ma

Question

A star (such as the sun) rotates about its axis every 25 days. The star has a mass of 2 × 1030 kg, and

a radius of 7×108 meters. You may treat the star as a uniform sphere (Isphere = (2/5)MR^2).

(a) What is the angular speed of the star?

(b) What is the angular momentum of the star?

(c) When the star runs out of fuel, it collapses and becomes a lot smaller. The details of this are quite messy. Assume the star did not shed mass when it collapsed (a good approximation for stars that do not go supernova) and became a smaller sphere with radius Rf . Given that the star now takes 1 second to rotate on its axis (instead of 25 days), calculate the new radius Rf .

Explanation / Answer

a) w (angular speed) = 2pi/ T= 2 (3.14)/ (25x 86400) = 2.91 x 10^ -6 rad /s

b) L = Iw = ( 2/5)MR^2 ( 2.91 x 10^ -6) = (0.4 ) ( 2x 10^30 )( 7 x 10^8) ^2 ( ( 2.91 x 10^ -6) = 114.072 x 10^ 40 kg m^2/s

c)we will use conservation of angular momnetum

initial momentum = final momentum

L final = ( 2/5 ) ( 2x 10^30 ) ( Rf)^2 (2x 3.14) = 5.024 x 10^ 30 Rf^2

5.024 x 10^ 30 Rf^2  = 114.072 x 10^ 40

Rf= 4.765 x 10^ 5 m apprx

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