Angular momentum conservation of two point masses

In summary, the conversation discusses the concept of angular momentum and how it applies to an object moving in a circular orbit. It is explained that when a force is applied to pull the object closer to the center, the tangential speed increases due to the force having a forward component. The concept of instantaneous center of rotation is also discussed, showing that a force acting towards the center of the spiral has a forward component, causing the object to speed up.
  • #1
adoion
55
0
Hi,

Lets suppose we have 2 point masses one fixed and imoveable the other rotateing in a perfect circle around the first imoveable one with constant speed.

Regardless of vich force is keeping the rotating mass on its circular orbit.
It may be a string or gravitational force or whatever.

The velocity of the rotating mass will allways be tangential to the circle the mass follows but the velocity vector intensity is the same as stated above (constant speed).

Now let's pull the rotating mass closer to the fixed mass, shorten the radius.
The conservation of angular momentum states that the the tangential spped of the rotating object should increase

If we aply a force orthogonal to the velocity vector to shorten the radius then this force could never ever change the intensity of the velocity.
Yet the conservation of angular momentum states different.

What is going on
 
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  • #2
If you are pulling the object in using a central force then that force is perpendicular to the object's original circular path. But it is not perpendicular to the object's spiral path as it is reeled in. The object speeds up because the force has a forward-pointing component along its path.

If, instead, you were pulling the object in using a force that was perpendicular to the object's spiral path then that force could not be centrally directed. In this case, angular momentum would not be conserved because the force would be an unbalanced external torque on the system. The circling object would retain its original speed, but would lose angular momentum.
 
  • #3
The spiral motion happends because the tangential velocity vector gets a component perpendicular to it because of the pulling force and the new vector is composed of the tangential component vitch remains constant and the ortogonal component vitch increases as long as rhe force is acting.

So there is no non-orthogonal component of the force on the tangential part of the velocity vector.

When force comes to hold the orthogonal component of the velocity dies out and one is left with the same velocity vector as at the begining.
Tangential to the now again circular path and same in magnitude as before.

So what is going on
 
  • #4
the tangential velocity vector gets a component perpendicular to it because of the pulling force

No. When it's moving in a spiral the instantaneous centre about which the object is rotating is NOT the center of the spiral. The instantaneous centre of rotation moves. See diagram. In this case the point is rotating around a point to the right of the centre of the spiral. This means that a force acting towards the centre of the spiral has a forward component.
 

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  • #5
?

Hello,

Thank you for your question. The conservation of angular momentum is a fundamental principle in physics that states that the total angular momentum of a closed system remains constant, unless acted upon by an external torque. In this case, the two point masses can be considered a closed system, as there are no external torques acting on them.

When you pull the rotating mass closer to the fixed mass, you are changing the radius of the circular orbit. This causes a change in the angular velocity of the rotating mass, as the distance from the center of rotation has decreased. However, in order to maintain the conservation of angular momentum, the tangential speed of the rotating mass must increase in order to compensate for the decrease in radius. This is because angular momentum is the product of the moment of inertia (which depends on the mass distribution and distance from the axis of rotation) and angular velocity. As the moment of inertia decreases, the angular velocity must increase in order to keep the angular momentum constant.

The force you mention that is applied orthogonal to the velocity vector is known as a centripetal force, which is responsible for keeping the rotating mass on its circular orbit. This force does not change the intensity of the velocity, but rather changes the direction of the velocity to keep it tangential to the circular path. The conservation of angular momentum still holds true in this case, as the centripetal force does not act as an external torque on the system.

I hope this explanation helps clarify the concept of angular momentum conservation in the context of two point masses. Please let me know if you have any further questions.
 

1. What is angular momentum conservation of two point masses?

Angular momentum conservation of two point masses is a physical law that states that the total angular momentum of a system of two point masses remains constant, unless an external torque is applied. It is based on the principle of conservation of angular momentum, which states that angular momentum is a conserved quantity in a closed system.

2. How is angular momentum conserved in a system of two point masses?

In a system of two point masses, the individual angular momenta of the two masses may change, but the total angular momentum of the system remains constant. This means that if one mass gains angular momentum, the other mass must lose an equal amount of angular momentum in order to maintain overall conservation.

3. What factors affect angular momentum conservation of two point masses?

The main factor that affects angular momentum conservation of two point masses is the external torque acting on the system. If there is no external torque, the total angular momentum will remain constant. Other factors that may affect the individual angular momenta of the two masses include their masses, velocities, and distance from each other.

4. How is angular momentum conserved in real-world situations?

In real-world situations, angular momentum conservation of two point masses can be observed in various scenarios such as planetary orbits, spinning objects, and collisions. In these situations, the total angular momentum of the system remains constant, even if the individual angular momenta of the masses change due to external forces.

5. Can angular momentum be transferred between two point masses?

Yes, angular momentum can be transferred between two point masses. This can occur through interactions such as collisions or gravitational forces. However, the total angular momentum of the system will remain constant, as long as no external torque is present.

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