Hi there, can you walk me through each part of the problem below? Can you help me understand the necessary steps to solve each part? Please also provide a response to each prompt so I can compare with my own solutions.

I have added a few formula reference that may be needed for the problem below. (Any unknown information can be found by searching on the internet/making reasonable or general assumptions)

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Practice Problem: Millisecond pulsars The fastest spinning stellar object known is a neutron star spinning at 716 Hz (1 hertz is a full rotation per second). It ashes us like a lighthouse beacon with a period of about 1.4 ms, hence the name millisecond pulsar. This extreme object has as much as twice the mass of the Sun compressed into a sphere of mostly neutrons with a radius at most 16 km. How could such a massive object. spin so fast? Fewer than 0.5% of all stars are more massive than 8 times the mass of the Sun. After these massive stars \"burn\" through their nuclear fuel, they lose their thermal pressure to support their massive weight and collapse in on themselves by their own gravity. Just as a gure skater speeds up by pulling her arms and feet close to her spin axis, the core of these massive stars spins up in one of the most dramatic events in the universe: a core-collapse supernova. Much of the mass of the star is blown off in an unbelievably large explosion7 while the core of the parent star collapses into a new neutron star. (a) What is the tangential speed of the equator of the neutron star? Give your answer as a percentage of the speed of light. (b) Astrophysicists can calculate that the radius of the stellar core shrinks by a factor of 512 to form the neutron star. \\Vhat can you say about the rotation rate of the stellar core before it collapsed, despite never observing it. directly? (c) Calculate the change in rotational kinetic energy. Express your answer as a multiple of the initial kinetic energy of the rotating stellar core? (d) (Optional) If you calculated a change in kinetic energy, where did that energy go or where did that energy come from? Work and Energy: Kinetic energy: K = =my Work: W = F . dr Work - Energy theorem: Wnet = AK Potential Energy (conservative Fc): W. = -AUc Conservation of Energy: Wnc = AK + AU Gravitational potential energy near the surface of the earth: U. = mgy Gmim2 Gravitational potential energy: UG = - r Spring potential energy: Usp = ka2 (for proper choice of coordinate system) Momentum and Impulse: Momentum: p = mu, Impulse: J = F dt ti Impulse-Momentum Theorem: J = Ap Conservation of Momentum: Ptot, f = Ptot, i (with no external forces)General: r(t) = x(t) ity(t) j+ z(t)k, dr du dar v (t ) = at ' a(t) = dt dt Newton's 2nd Law: For a an object of mass m: _ Fext = Fnet = ma Common Forces: Force due to gravity near surface of the earth: F , = mg Universal gravitation: |Fal = Gmim2 72 Spring force: Fsp = kell- lol in the direction to restore equilibrium Static friction: Kinetic friction: |FS | = HK N Kinematics with constant acceleration: u(t) = vo ta . (t -to) r(t) = ro+ vo . (t -to)+ za. (t-to)2 For a single dimension / axis x, we can also write: Uf x = Vox + 2ax(x5 -20) Simple Harmonic Oscillators: For a spring-mass system (k, and m): x(t) = Acos(wt + 4) 2 7T Where: W = T and T is the period of motion Circular Motion: de Arc Length: s = re Angular velocity: W = dt v = wr Centripetal acceleration: ac = = warReference for mements of inertia Axis Hoop about cylinder axis l = MR2 Axis Solid cylinder (or disk) about " cylinder axis , = ?- 2 Axis _ Thin rod about axis through i center J. to length it? \"'th Axis Solid sphere 2F? about any diameter _ zone I 5 Axis Hoop about t. any diameter Annular cylinder {or ring} about cylinder axis :=%tsi+s) Solid cylinder (or disk} about " oentral diameter Thin rod about axis through one i end i to length _ MP ' T Axis Thin . 2R spherical shell about any diameter l = ans? 3 Axis Slab about i axis through center b a If : M 12 Figure 10.21] Values of rotational inertia for common shapes of objects