Question

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

b) What would be its final KE in terms of its initial KE of today? (KEfinal / KEinitial) =

Answer 1

a )

using I_ii = I_ff  

I_i = 2/5 M_oR_o²

I_f = 2/5 ( 3M_o/4) (R/400)²

2/5 M_oR_o²_i = 2/5 ( 3M_o/4) (R/400)²_f   

_i = ( 3/4) (1/400)²_f   

2 X 3.14 / 30 X 24 X 3600 = 4.6875 X 10^-6 X _f

_f = 0.516 rad/sec

b )

(KE_final / KE_initial) = 1/2 I_ff² / 1/2 I_ii²

= 1/2 X 2/5 X ( 3M_o/4) (R/400)² X 0.516² / 2/5 M_oR_o² X ( 2 X 3.14 / 30 X 24 X 3600)²  

(KE_final / KE_initial) = 6.24 X 10^-7/ ( 2 X 3.14 / 30 X 24 X 3600)²  

(KE_final / KE_initial) = 106306.88