Question

Suppose a star the size of our Sun, but with mass 5.0 times as great, were rotating at a speed of 1.0 revolution every 15 days. If it were to undergo gravitational collapse to a neutron star of radius 14 km , losing three-quarters of its mass in the process, what would its rotation speed be? Assume also that the thrown- off mass carries off either

Part A) No angular momentum

Part B) its proportional share three-quarters of the initial angular momentum

Answer 1

A)

Mi = initial mass = 5 x 1.989 x 1030 kg

Ri = initial radius = 6.9634 x 108 m

wi = initial angular velocity = 1 rev/15 days = 2 pi /(15 x 24 x 3600) = 4.85 x 10-6 rad/s

Mf = final mass = (1/4) (5 x 1.989 x 1030) kg

Rf = final radius = 14 km = 14000 m

wf = final angular velocity = ?

Using conservation of angular momentum

(2/5) Mi Ri2 wi = (2/5) Mf Rf2 wf

Mi Ri2 wi = Mf Rf2 wf

(5 x 1.989 x 1030) (6.9634 x 108)2 (4.85 x 10-6) = ((1/4) (5 x 1.989 x 1030)) (14000)2 wf

wf = 4.8 x 104 rad/s

B)

Using conservation of momentum

(1/4) (2/5) Mi Ri2 wi = (2/5) Mf Rf2 wf

(1/4) Mi Ri2 wi = Mf Rf2 wf

(1/4) (5 x 1.989 x 1030) (6.9634 x 108)2 (4.85 x 10-6) = ((1/4) (5 x 1.989 x 1030)) (14000)2 wf

wf = 1.2 x 104 rad/s