Ratios of Initial to Final Energy/Momentum/Velocity

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SUMMARY

The discussion focuses on the physics of a rotating star collapsing into a pulsar, specifically analyzing the ratios of angular momentum, angular velocity, rotational kinetic energy, and the period of rotation before and after the collapse. The radius of the star after collapse is 4.00 x 10-4 times its original radius, with mass remaining constant. The key equations for angular momentum, angular velocity, and kinetic energy are applied to derive the necessary ratios and period changes, providing a clear framework for solving the problem.

PREREQUISITES
  • Understanding of angular momentum in rotational dynamics
  • Familiarity with the concept of rotational kinetic energy
  • Knowledge of the relationship between radius and angular velocity
  • Basic grasp of gravitational collapse in astrophysics
NEXT STEPS
  • Calculate the ratio of angular momentum using the formula L = Iω
  • Explore the relationship between angular velocity and radius in rotating systems
  • Investigate the equations governing rotational kinetic energy, specifically KE = 0.5 Iω²
  • Determine the new period of rotation using T = 2π/ω
USEFUL FOR

Students in physics, astrophysics enthusiasts, and anyone studying the dynamics of rotating bodies and gravitational collapse will benefit from this discussion.

Jtappan
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Homework Statement



A rotating star collapses under the influence of gravitational forces to form a pulsar. The radius of the star after collapse is 4.00 10-4 times the radius before collapse. There is no change in mass. In both cases the mass of the star is uniformly distributed in a spherical shape.
(a) What is the ratio of the angular momentum of the star after collapse to before collapse?


(b) What is the ratio of the angular velocity of the star after collapse to before collapse?


(c) What is the ratio of the rotational kinetic energy of the star after collapse to before collapse?


(d) If the period of the star's rotation before collapse is 5.00 107 s, what is its period after collapse?
____ s


Homework Equations





The Attempt at a Solution



I am having trouble imputing this into my online homework. Could you give me an example as to how I could put this into my online homework??
 
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