Very Challenging Problem For Physics Prodigies Only!!?

Question

1) A star with the mass (M = 2.0 x 10^30 kg) and size (R = 3.5 x 10^8 m) of our sun rotates once every 35.0 days. After undergoing gravitational collapse, the star forms a pulsar that is observed by astronomers to emit radio pulses every 0.200 s. By treating the neutron star as a solid sphere, deduce its radius.

2) What is the speed of a point on the equator of the neutron star? Your answer will be somewhat too large because a star cannot be accurately modeled as a solid sphere.

Answer 1

r = 3.5 x 10^8 m x (35 day/.2 sec) = 556 m

circ = 2πr = 3,491 m

equatorial speed = 17,453 m/sec

Answer 2

19 and 28

Answer 3

1) L₀ = I₀ω₀ = Iω = L

L₀ = [(2/5)mR₀²][2π/T₀]

L = [(2/5)mR²][2π/T] = [(2/5)mR₀²][2π/T₀]

R²/T = R₀²/T₀

R = R₀√(T/T₀) = (3.5x10^8m)√(0.2s / 3.02x10^6s)

= 9.0x10^4 m

2) v = (2πR)/T = 2π(9.0x10^4m)/(0.2s)

=2.83x10^6 m/s