Star collapse
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The following quantities appear in the problem:
Trägheitsmoment \(J, \Theta, I\) / Drehimpuls \(\vec L\) / Winkelgeschwindigkeit / Kreisfrequenz \(\omega\) /
The following formulas must be used to solve the exercise:
\(L = J \omega \quad \)
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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.
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.