Angular momentum - Planet exercise

  • #1

Homework Statement



Dear all,

This is my first post and I need some help. The exercise I am trying to solve is this one:

A star has a radius of 6 × 10^8 m and a period of rotation of 30 days. Eventually it becomes a neutron star with a radius of 10^4 m and a period of 0.1 s. If the mass has not changed, find the ratio of initial and final (a) angular momentum and (b) kinetic energy.

Homework Equations



I know that I must use for angular momentum L = Iω and for kinetic energy K = 1/2 Iω^2, where I is the moment of inertia. I assumed the body geometry as a sphere.

The Attempt at a Solution



I made all the substitutions and in fact I got the right answers (Lini/Lfin = 139 and Kini/Kfin=5.4x10^-6). My question: in this exercise, why the angular momentum is not conserved? Can anybody provide some physical explanation?
 

Answers and Replies

  • #2
gneill
Mentor
20,846
2,817

Homework Statement



Dear all,

This is my first post and I need some help. The exercise I am trying to solve is this one:

A star has a radius of 6 × 10^8 m and a period of rotation of 30 days. Eventually it becomes a neutron star with a radius of 10^4 m and a period of 0.1 s. If the mass has not changed, find the ratio of initial and final (a) angular momentum and (b) kinetic energy.

Homework Equations



I know that I must use for angular momentum L = Iω and for kinetic energy K = 1/2 Iω^2, where I is the moment of inertia. I assumed the body geometry as a sphere.

The Attempt at a Solution



I made all the substitutions and in fact I got the right answers (Lini/Lfin = 139 and Kini/Kfin=5.4x10^-6). My question: in this exercise, why the angular momentum is not conserved? Can anybody provide some physical explanation?
Hi Curious2013; Welcome to Physics Forums.

The reason why you found angular momentum was not conserved is an artifact of the problem author's choice of initial and final conditions; you're given radii and periods of rotation without explanation of how they might be related; They might as well have been given for two entirely distinct and unrelated objects which happened to have the same mass. Besides, the problem makes no mention of the physics that has to occur to go from one state to the other -- physics that in "real life" would involve a nova event and ejection of a good chunk of mass and radiation, and interaction of enormous magnetic fields with the ejecta. Angular momentum is always conserved IF you can keep track of all the bits!

I suspect that this was intended to be more an exercise in setting up ratios and seeing how "missing values" and constants can cancel out to yield tidy simplifications, rather than a exploration of neutron star physics.
 
  • #3
Hi Curious2013; Welcome to Physics Forums.

The reason why you found angular momentum was not conserved is an artifact of the problem author's choice of initial and final conditions; you're given radii and periods of rotation without explanation of how they might be related; They might as well have been given for two entirely distinct and unrelated objects which happened to have the same mass. Besides, the problem makes no mention of the physics that has to occur to go from one state to the other -- physics that in "real life" would involve a nova event and ejection of a good chunk of mass and radiation, and interaction of enormous magnetic fields with the ejecta. Angular momentum is always conserved IF you can keep track of all the bits!

I suspect that this was intended to be more an exercise in setting up ratios and seeing how "missing values" and constants can cancel out to yield tidy simplifications, rather than a exploration of neutron star physics.

Dear gneill

Thanks for the reply!
 

Related Threads on Angular momentum - Planet exercise

  • Last Post
Replies
2
Views
6K
  • Last Post
Replies
10
Views
5K
Replies
2
Views
3K
  • Last Post
Replies
16
Views
2K
  • Last Post
Replies
9
Views
3K
Replies
2
Views
358
  • Last Post
Replies
2
Views
341
  • Last Post
Replies
0
Views
3K
Replies
1
Views
78
Top