Rotational motion and law of gravity

In summary, the conversation is discussing how to determine the greatest possible angular speed of a neutron star with a mass twice that of the sun and a radius of 10.0 km, so that the matter at its surface on the equator is held in orbit by the gravitational force. The participants discuss using the equations for gravitational force and centripetal force, but are unsure of what to do next. They list all the given variables as R, V, M, m, and G.
  • #1
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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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  • #2
...still lost... idk what to do...
 
  • #3
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.
 
  • #4
ok you so i get GMm/r^2=mV^2/R, but still don't know what to do
 
  • #5
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=?
 

1. What is rotational motion?

Rotational motion is the movement of an object around an axis or point, where the object maintains a fixed distance from the axis while its orientation changes.

2. How is rotational motion different from linear motion?

Rotational motion involves the movement of an object along a circular path, while linear motion involves the movement of an object in a straight line. Rotational motion also involves the concept of torque, which is not present in linear motion.

3. What is the law of gravity?

The law of gravity states that any two objects in the universe attract each other with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

4. How does the law of gravity relate to rotational motion?

The law of gravity plays a crucial role in rotational motion as it is responsible for the gravitational force that acts on an object, causing it to rotate around a central axis. This is seen in the rotation of planets around the sun and the rotation of satellites around a planet.

5. How can the law of gravity be applied in real-life situations?

The law of gravity is used in various applications, such as predicting the trajectory of a projectile, understanding the motion of celestial bodies, and designing satellites and spacecraft. It also plays a significant role in engineering and construction, particularly in designing structures that can withstand gravitational forces.

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