Rotational motion and law of gravity

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SUMMARY

The discussion focuses on calculating the maximum angular speed of a neutron star, specifically one with a mass twice that of the Sun and a radius of 10.0 km. The gravitational force must equal the centripetal force acting on the matter at the star's equator, leading to the equation GMm/r² = mV²/R. Participants emphasize the importance of correctly identifying and applying the relevant physical constants and variables to solve for angular speed.

PREREQUISITES
  • Understanding of gravitational force and centripetal force concepts
  • Familiarity with the equation of motion for circular orbits
  • Knowledge of the gravitational constant (G) and its application
  • Basic algebraic manipulation skills for solving equations
NEXT STEPS
  • Study the derivation of the gravitational force equation (Fg = GMm/r²)
  • Learn about centripetal acceleration and its relationship to angular speed
  • Explore the properties of neutron stars and their formation
  • Investigate the implications of angular momentum conservation in astrophysics
USEFUL FOR

Students studying astrophysics, physics educators, and anyone interested in the dynamics of celestial bodies, particularly neutron stars and their rotational characteristics.

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Homework Statement


Neutron stars are extremely dense objects that are formed from the remnants of supernova explosions. many rotate very rapidly. suppose that the mass of a certain spherical neutron star is twice the mass of the sun and its radius is 10.0 km. determine the greatest possible angular speed the neutron star can have so that the matter at the its surface on the equator to be just held in orbit by the gravitational force.


Homework Equations





The Attempt at a Solution


i no that the gravtiational force must equal the Force
so GM/r^2=mV^2/ R, but where do i go fom here I am lost!
 
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...still lost... idk what to do...
 
i no that the gravtiational force must equal the Force

So the gravitational force must equal the net force? Which is the centripetal force.
Fg=Fc
So I think you got this far already, but it looks as though you made a small mistake on this next step when you came up with this equation:
GM/r^2=mV^2/ R
You may have forgotten to either include a mass term or cross one out.. look at the equations for Fg and Fc again.
 
ok you so i get GMm/r^2=mV^2/R, but still don't know what to do
 
What is the question asking us to solve for?

Do you have everything you need to solve for it? I often make a list of everything that's been given, even before starting.

R=?
V=?
M=?
m=?
G=?
 

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