Question

You are working in an observatory, taking data on electromagnetic radiation from neutron stars. You happen to be analyzing results from a neutron star similar to the one in the Formation of a Neutron Star example, verifying that the period of a 11.0 km radius neutron star is indeed 2.5 s. You go through weeks of data showing the same period. Suddenly, as you analyze the most recent data, you notice that the period has decreased to 1.8 s and remained at that level since that time. You ask your supervisor about this, who becomes excited and says that the neutron star must have undergone a glitch, which is a sudden shrinking of the radius of the star, resulting in a higher angular speed. As she runs to her computer to start writing a paper on the glitch, she calls back to you to calculate the new radius of the star (in km), assuming it has remained spherical. She is also talking about vortices and a superfluid core, but you don't understand those words.

Answer 1

Given,

R₁ = 11 Km,

T₁ = 2.5 s, T₂ = 1.8 s

By the conservation of angular momentum,

I₁w₁ = I₂w₂

(2/5) * MR₁² * (2/T₁) = (2/5) * M R₂² * (2/ T₂)

R₁² / T₁ = R₂² / T₂

(11)² / 2.5 =  R₂² / 1.8

R₂² = 87.12

R₂ = 9.334 Km