Exercise
https://texercises.com/exercise/star-collapse/
Question
Solution
Short
Video
\(\LaTeX\)
Need help? Yes, please!
The following quantities appear in the problem:
The following formulas must be used to solve the exercise:
No explanation / solution video to this exercise has yet been created.

Visit our YouTube-Channel to see solutions to other exercises.
Don't forget to subscribe to our channel, like the videos and leave comments!
Exercise:
Astronomers often detect stars that are rotating extremely rapidly known as neutron stars. These stars are believed to have formed from the inner core of a larger star that collapsed due to its own gravitation to a star of very small radius and very high density. Before collapse suppose the core of such a star is the size of our Sun rapproxekm with mass . times as great as the Sun and is rotating at a speed of . revolution every days. If it were to undergo gravitational collapse to a neutron star of radius km what would its rotation speed be? Ase the star is a uniform sphere at all times.

Solution:
The mass of the neutron star is m M_SunIndex ekg ekg. Hence its moment of inertia before the gravitational collapse is I_ fracm_r^ frac ekg em^ .ekilogrammetersquared. Its angular velocity is omega_ pi f pi .Hz .radianpersecond. After the gravitational collapse the stars moment of inertia is due to its much smaller diameter J_ fracm_r^ frac ekg em^ .ekgm^. The conservation law for the angular momentum gives L_ &mustbe L_ J_ omega_ J_omega_ omega_ fracJ_J_ omega_ fracpq.ekilogrammetersquared.ekilogrammetersquared .radianpersecond .eradianpersecond. That are approximately numpr revolutions per second.
Meta Information
\(\LaTeX\)-Code
Exercise:
Astronomers often detect stars that are rotating extremely rapidly known as neutron stars. These stars are believed to have formed from the inner core of a larger star that collapsed due to its own gravitation to a star of very small radius and very high density. Before collapse suppose the core of such a star is the size of our Sun rapproxekm with mass . times as great as the Sun and is rotating at a speed of . revolution every days. If it were to undergo gravitational collapse to a neutron star of radius km what would its rotation speed be? Ase the star is a uniform sphere at all times.

Solution:
The mass of the neutron star is m M_SunIndex ekg ekg. Hence its moment of inertia before the gravitational collapse is I_ fracm_r^ frac ekg em^ .ekilogrammetersquared. Its angular velocity is omega_ pi f pi .Hz .radianpersecond. After the gravitational collapse the stars moment of inertia is due to its much smaller diameter J_ fracm_r^ frac ekg em^ .ekgm^. The conservation law for the angular momentum gives L_ &mustbe L_ J_ omega_ J_omega_ omega_ fracJ_J_ omega_ fracpq.ekilogrammetersquared.ekilogrammetersquared .radianpersecond .eradianpersecond. That are approximately numpr revolutions per second.
Contained in these collections:
  1. Neutronenstern by TeXercises
    1 | 2
  2. 5 | 11

Attributes & Decorations
Branches
Momentum
Tags
angular, conservation, inertia, law, mechanics, moment, momentum, of, physics, rotation
Content image
Difficulty
(2, default)
Points
2 (default)
Language
ENG (English)
Type
Calculative / Quantity
Creator uz
Decoration
File
Link