Rotational Motion: Supernova to Pulsar Transformation

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SUMMARY

The discussion centers on the transformation of a supernova into a pulsar, specifically analyzing the angular velocities and rotational kinetic energy involved. The pulsar, with a mass of 2.2 solar masses and a radius of 10 km, rotates at 75 revolutions per second, leading to an angular velocity calculation of approximately 471.24 rad/s. The progenitor star, with a mass of 15 solar masses and a radius of 7 x 1010 m, is suggested to have an initial angular velocity of zero, which is incorrect; it must be calculated based on conservation of angular momentum. The rotational kinetic energy of the pulsar is derived from its mass and radius, emphasizing the importance of these calculations in understanding stellar evolution.

PREREQUISITES
  • Understanding of angular velocity and its calculation
  • Knowledge of conservation of angular momentum
  • Familiarity with rotational kinetic energy formulas
  • Basic astrophysics concepts regarding supernovae and pulsars
NEXT STEPS
  • Calculate the angular momentum of the pulsar using its mass and radius
  • Explore the relationship between supernova explosions and pulsar formation
  • Investigate the implications of conservation of angular momentum in astrophysics
  • Learn about the physical properties and behaviors of pulsars
USEFUL FOR

Astronomy students, astrophysicists, and educators interested in stellar evolution and the physics of supernovae and pulsars will benefit from this discussion.

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Homework Statement


A supernova is the explosion of a large star. The progenitor, the star just before it explodes has a mass of 15 solar masses and a radius of 7*10^10m. After the supernova, a pulsar is left over. The pulsar has a mass of 2.2 solar masses and a radius of 10km.

a) If the pulsar rotates 75 times a second what is its angular velocity.
b) What was the angular velocity of the proginator.
c) What is the rotational kinetic energy of the pulsar.


Homework Equations





The Attempt at a Solution


is my work correct
a) angular velocity pulsar = (2pi * 75) / sec
b) would the angular velocity of the proginator be 0 i am not sure how to do this one.
c) K =.5*(2.2)*((10,000m)^2)
 
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I'd say in b) they are wanting you to calculate the angular momentum of the spinning pulsar given the final geometry and then apply that back to the geometry and mass of the proginator, relying on conservation of angular momentum.
 

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