Question

Suppose a star of mass M at the end of its evolution collapses into a white dwarf, losing half its mass. In the cataclysmic end process the mass thrown off carries no angular momentum, but the core collapses to 1.0% of the original size of the star.

a. If the original star rotated at a rate of once per 30 days, what would its new rotation rate be?

b.

What would be the ratio of its final rotational kinetic energy be to its original rotational kinetic

energy?

Answer 1

let R1 is the initail radius.

final radius, R2 = R1/100 = 0.01*R1

a) Apply conservation of angular momentum

I2*w2 = I1*w1

(1/2)*(2/5)M*R2^2*(2*pi/T2) = (1/2)*(2/5)*M*R1^2*(2*pi/T1)

R2^2/T2 = R1^2/T1

(0.01*R1)^2/T2 = R1^2/T1

T2 = T1*0.01^2

= 30*0.01^2

= 0.003 days

= 0.003*24*60*60 s

= 259.2 s (or) 4.32 min <<<<<<<<----------------Answer

b) KEf = (1/2)*I2*w2^2

= (1/2)*(2/5)*M*R2^2*(2*pi/T2)^2

KEi = (1/2)*I1*w1^2

= (1/2)*(2/5)*M*R1^2*(2*pi/T1)^2

KEf/KEi = (R2/T2)^2*(T1^2/R1^2)

= (R1*0.01/R1)^2*(T1/T2)^2

= 0.01^2*1/(0.01^2)^2

= 10^4   <<<<<<<<----------------Answer