Suppose our Sun eventually collapses into a white dwarf, in the process losing a

Question

Suppose our Sun eventually collapses into a white dwarf, in the process losing about two thirds of its mass and winding up with a radius 4.0 percent of its existing radius. What would its new rotation rate be? (Take the Sun's current period to be about 30 days.)

Suppose our Sun eventually collapses to a white dwarf, in the process losing about two thirds of its mass and winding up with a radius 4.0 percent of its existing radius. What would its new rotation rate be? (Take the Sun's current period to be about 30 days.) ra What would be its final KE in terms of its initial KE of today? (KE final KE

Explanation / Answer

We know that angular momentum is conserved, so

Li = Lf

Ii wi = If wf

Ii = 2/5 M R^2

If = 2/5 (2M/3) (R/100)^2

(2/5 M R^2) wi = (2/5 2M/3 (R/400)^2 wf

wi = (1/240000) wf

wf = 240000 wi

wi = 2 pi/T = 2 x 3.14 / (2.59 x 10^6) = 2.42 x 10^-6

wf = 240000 x wi = 2.4 x 10^5 x 2.42 x 10^-6 = 5.81

Hence, wf = 5.81 rad/s

b)KEi = 1/2 Ii wi^2

KEi = 1/2 (2/5 M R^2) wi^2

KEf = 1/2 (2/5 2M/3 (R/400)^2 wf^2

KEf/KEi = 1/2 (2/5 2M/3 (R/400)^2 wf^2/ 1/2 (2/5 M R^2) wi^2

KEf/KEi = 2 wf^2/3 x 160000 x wi^2

KEf/KEi = 2 x 5.81^2/2.4 x 10^5 x (2.42 x 10^-6)^2 = 4.8 x 10^7

Hence, KEf/KEi = 4.8 x 10^7

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