Question

In a little over 5 billion years, our Sun will collapse to a white dwarf approximately...

In a little over 5 billion years, our Sun will collapse to a white dwarf approximately 16,000 km in diameter. (Ignore the fact that the Sun will lose mass as it ages.) (a) What will our Sun’s angular momentum and rotation rate be as a white dwarf? (Express your answers as multiples of its present-day values.) (b) Compared to its present value, will the Sun’s rotational kinetic energy increase, decrease, or stay the same when it becomes a white dwarf? If it does change, by what factor will it change? The radius of the Sun is presently 6.96 * 108 m.

Homework Answers

Answer #1

a)

Ms = mass of sun

Rs = initial radius of sun = 6.96 x 108 m

Rd = final radius of whitedwarf = 8000 km = 8 x 106 m

wi = present rotation rate

wf = final rotation rate

Angular momentum of Sun = angular momentum of sun as white dwarf = (2/5) Ms Rs2 Wi2

using conservation of angular momentum

Angular momentum of Sun = angular momentum of sun as white dwarf

(2/5) Ms Rs2 Wi = (2/5) Ms Rd2 Wf

Wf = R2s Wi/R2d = (6.96 x 108 /(8 x 106 ))2 Wi = 7569 Wi

b)

as the sun becomes white dwarf , its moment of inertia decreases and rotation speed increases , hence the rotational kinetic energy will increase

change = (2/5) Ms Rs2 Wi2 - (2/5) Ms Rd2 Wf2 = (2/5) Ms Rs2 Wi2 - (2/5) Ms (87 Rs)2 (7569 Wi)2

= (2/5) Ms Rs2 Wi2 (1 - 87^2 7569^2) = - 4.34 x 1011

factor = 4.34 x 1011

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