A star with mass m, period of Ti= 30 days, and a radius ri=1E4 collapses into a

Question

A star with mass m, period of Ti= 30 days, and a radius ri=1E4 collapses into a neutron star with a radius of rf= 3.0 km.

a) How much angular momentum, Li, does the star have before it collapses(formula)? a) IiWi b) mivi c) riTi d) mri^2

b) What is the rotation rate, wi, of the star before collapsing(formula)? a) mri^2 b) riTi c) 2pifi d) 2pi/Ti

c) Suppose we model the star as a solid sphere of radius ri with moment of inertia 0.4mri^2. What does or description of Li read now?

d) How much angular momentum, Lf, does the star have after it collapses? a) mrf^2 b) mfvf c) rfTf d) Ifwf

e) What is the rotation rate, wf, of the star after collapsing? a) mrf^2 b) rfTf c) 2piff d) 2pi/Tf

f) The neutron star is also shaped like a sphere. What does Lf read?

g) Assuming angular momentum is conserved during collapse (also a good assumption), what is our prediction for the period of the neutron star (Tf)? a) pir^2 b) 2piTi c) 0.4Ti d) Ti(rf/ri)^2

h) What is Tf in units of days?

I) What is Tf in units of seconds?

Explanation / Answer

a)

angular momentum L = Ii*wi

option (a)

(b)

wi = 2pi/Ti

1/Ti = frequency fi

wi = 2*pi*fi <<--answer

option(c)

c)

Li = Ii*wi = 0.4*m*ri^2*2*pi*(1/(30*24*60*60))

Li = m*ri^2*9.67*10^-7 kg m^2/s

d)

Lf = Li = If*wf

option (d)

+++++++++

e)

wf = 2*pi*ff

option (c)

++++++++

f)

Lf = Li = m*ri^2*9.67*10^-7 kg m^2/s

++++++

g)

Lf = Li

0.4*m*rf^2*2*pi*(1/Tf) = 0.4*m*ri^2*2*pi*(1/Ti)

rf^2/Tf = ri^2/Ti

Tf = (rf/ri)^2*Ti <<----answer

option (d)

+++++++++

h) Tf = 30*(3000/10000)^2 = 2.7 days

i) Tf = 2.7*24*60*60 = 233280 s

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