Answer to Question #83807 in Physics for Nethmini Bandara

Question

Two stars A and B of uniform density have equal radii star A having twice the mass of star B is spinning 3 times faster than star B,
The ratio,
Angular momentum of star A divide by angular momentum of star B

Answer 1

The stars can be described as solid spheres, so their moments of inertia are:

I_B=2/5 m_B r^2, I_A=2/5 m_A r^2=2/5·2m_B·r^2.

Their angular momenta:

L_B=I_B ω_B,L_A=I_A·ω_A=I_A·3ω_B.

Calculate the ratio: divide the angular momentum of star A by the angular momentum of star B:

L_A/L_B =(I_A·3ω_B)/(I_B ω_B )=(2/5·2m_B·r^2·3ω_B)/(2/5·m_B·r^2·ω_B )=6.