Suppose our Sun eventually collapses into a white dwarf, losing about half its m

Question

Suppose our Sun eventually collapses into a white dwarf, losing about half its mass in the process, and winding up with a radius 1.0% of its existing radius.

Part A

Assuming the lost mass carries away no angular momentum, what would the Sun's new rotation rate be? Take the Sun's current period to be about 30 days.

Express your answer using three significant figures and include the appropriate units.

wf=

Part B

What would be its final kinetic energy in terms of its initial kinetic energy of today?

Express your answer using two significant figures.

KEf =

xKEi

KEf =

xKEi

Explanation / Answer

Angular momentum is conserved -- always.
L = I?
For an homogeneous sphere,
I = 2/5 mr^2
L1 = L2
m1 = 2*m2
r1 = 100 r2

L1 = L2
I1 ?1 = I2 ?2
2/5 m1 (r1)^2 ?1 = 2/5 m2 (r2)^2 ?2
?2 = ?1 (m1/m2) (r1/r2)^2
?2 = ?1 (2) (100)^2
?2 = 20000 ?1

Given the sun has a period of 30 days, the new period would be
P2 = 30days/20000 = 129.6 seconds

.......
KE = 1/2 I ?^2

KE2 = KE1 * (m2/m1) (r2/r1)^2 (?2/?1)^2
KE2 = 20,000 KE1

Note: The additional energy comes from the gravitational collapse. The mass is has much less Potential energy

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