Linear momentum conservation vs angular momentum conservation

In summary, the conservation of linear momentum implies the conservation of angular momentum, as seen in the example of off-center impact and subsequent adhesion. However, while linear momentum conservation is instantaneous in real time, angular momentum conservation requires the interaction of two masses to be physically observed. Therefore, angular momentum conservation is not implied but rather has a physical, observable reality. This suggests a qualitative difference between the two forms of momentum conservation.
  • #1
Shaw
46
3
If linear momentum conservation is instantaneous in real time, then angular momentum conservation must be too. In other words, if you want to get something spinning, then you must physically turn something else in the opposite direction. Angular momentum conservation can't be implied, it has to have a physical, observable reality. Is this correct?
 
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  • #2
Somewhat unclear, but that sounds good.

Maybe?

Are you trying to say that the conservation of linear momentum implies the conservation of angular momentum?

In that case, I could buy into that. It might be preferable to show this more rigorously by making arguments that rigid rotators are collections of point particles which obey linear momentum conservation.
 
  • #3
We can use linear momentum conservation to induce angular momentum in another body through off center impact and subsequent adhesion. After impact, a non-rotating mass is moving in one direction, while a rotating mass is moving off in the other. Linear momentum is conserved, but in real time we have net angular momentum.

Angular momentum conservation is implied because of the misaligned centers of mass relative to the direction of travel, but remains a potential until the two centers are brought to a halt relative to each other. So how can angular momentum be the direct translation of linear momentum to rotating systems? There seems to be a qualitative difference here. It looks like total conservation remains a property of space until the 2 masses interact.
 

1. What is the difference between linear momentum and angular momentum conservation?

Linear momentum conservation refers to the principle that the total momentum of a system remains constant in the absence of external forces. This means that if no external forces act on a system, the total momentum before an event will be equal to the total momentum after the event. Angular momentum conservation, on the other hand, refers to the principle that the total angular momentum of a system remains constant when no external torque acts on the system.

2. How are linear momentum and angular momentum related?

Linear momentum and angular momentum are both measures of the motion of an object. Linear momentum is the product of an object's mass and its velocity, while angular momentum is the product of an object's moment of inertia and its angular velocity. In simpler terms, linear momentum refers to the motion of an object in a straight line, while angular momentum refers to the motion of an object around a fixed axis.

3. Are linear momentum and angular momentum always conserved?

In an ideal, isolated system with no external forces or torques, both linear momentum and angular momentum will be conserved. However, in real-world situations, external forces and torques are often present and can cause changes in both linear and angular momentum. This means that while these principles are fundamental laws of physics, they may not always hold true in practical applications.

4. Can linear and angular momentum be converted into each other?

No, linear and angular momentum are separate and distinct quantities that cannot be converted into each other. However, in certain situations, linear momentum may be transformed into angular momentum, such as when a rotating object experiences a change in its moment of inertia. This is known as angular impulse.

5. How can the conservation of linear and angular momentum be applied in real-world scenarios?

The conservation of linear and angular momentum is a fundamental principle that is applied in many areas of physics, including mechanics, fluid dynamics, and astrophysics. For example, it is used to analyze the motion of objects in collisions, the behavior of spinning objects, and the movement of celestial bodies. It is also a key concept in engineering, as it allows for the prediction and control of the motion of complex systems.

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