A star with mass m, period Ti = 30 days, and radius ri = 1E4 km collapses into a neutron star (Links to an external site.) with a radius of rf = 3 km. Our goal will be to determine the period Tf of the neutron star. Useful formulae: Li=Lf; L=Iω; ω=2πf=2π/T; Isphere=2/5mr^2. 1.How much angular momentum Li does the star have before it collapses? 2. What is the rotation rate ωi of the star before collapsing? 3. Suppose we model the star as a solid sphere of radius ri with moment of inertia 2/5mri2 (a good assumption). What does our description of Li read now?

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A star with mass m, period Ti = 30 days, and radius ri = 1E4 km collapses into a neutron star (Links to an external site.) with a radius of rf = 3 km. Our goal will be to determine the period Tf of the neutron star. Useful formulae: Li=Lf; L=Iω; ω=2πf=2π/T; Isphere=2/5mr^2.

1.How much angular momentum Li does the star have before it collapses?

2. What is the rotation rate ωi of the star before collapsing?

3. Suppose we model the star as a solid sphere of radius ri with moment of inertia 2/5mri2 (a good assumption). What does our description of Li read now?

4.How much angular momentum Lf does the star have after it collapses?


5. What is the rotation rate ωf of the star after collapsing?
 
6.The new object, a neutron star, is also shaped like a sphere. What does Lf read?
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7.Assuming angular momentum is conserved during collapse (also a good assumption), what is our prediction for the period of the neutron star, Tf?

 
8. What is Tf in units of days?
 
9. What is Tf in units of seconds?
 
10. What is the physical interpretation of Tf?

 
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