Conservation of energy and angular momentum

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Discussion Overview

The discussion revolves around the conservation of energy and angular momentum in the context of two identical gears interacting through an inelastic collision. Participants explore the implications of angular momentum conservation and the transformation of energy forms during the interaction.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • Some participants assert that when two identical gears are attached, angular momentum is conserved, leading to a new angular velocity w' that equals 0.5w.
  • Others argue that kinetic energy is not conserved in this scenario, characterizing the interaction as an inelastic collision where energy is transformed into heat and sound.
  • A participant mentions that total energy remains constant but can change forms, including potential energy and various types of kinetic energy.
  • Some participants note that the 'lost' energy in the system is exactly half of the total energy, particularly in the case of equal gears.
  • One participant draws a parallel to linear momentum and kinetic energy, discussing how momentum is conserved in collisions while kinetic energy is not, and questions why objects cannot simply come to rest after an inelastic collision.
  • Another participant responds to this question by explaining that momentum must be absorbed by another object, using the example of a car coming to rest due to friction and air drag, which transfers momentum to the Earth.

Areas of Agreement / Disagreement

Participants generally agree that angular momentum is conserved while kinetic energy is not, but there is ongoing debate about the implications of these principles and the nature of energy transformation in inelastic collisions.

Contextual Notes

Participants express uncertainty regarding the specific mechanisms of energy transformation and the conditions under which momentum conservation applies, particularly in complex interactions.

pixel01
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Hi all,

There are 2 identical gears which are in the same axis. At first gear #1 rotates at angular velocity w, while gear #2 stays still. Now the gears are attached and rotate at the same angular velocity w'.

Because the angular momentum is conserved so w' = 0.5 w
But then the kinetic energy is not conserved?
 
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pixel01 said:
Hi all,

There are 2 identical gears which are in the same axis. At first gear #1 rotates at angular velocity w, while gear #2 stays still. Now the gears are attached and rotate at the same angular velocity w'.

Because the angular momentum is conserved so w' = 0.5 w
But then the kinetic energy is not conserved?

No, kinetic energy is not conserved here. It is kind of inelastic collision.

In linear collisions of two equal masses, when they stick together, it means inelastic collision.

A part of the initial energy is spent on heat to stick the bodies together.
 
pixel01 said:
Hi all,

There are 2 identical gears which are in the same axis. At first gear #1 rotates at angular velocity w, while gear #2 stays still. Now the gears are attached and rotate at the same angular velocity w'.

Because the angular momentum is conserved so w' = 0.5 w
But then the kinetic energy is not conserved?

This is true. Total energy stays constant. It's free to change form from potential to kinetic, or even different types of kinetic energy - the rotational kinetic energy in this example, linear kinetic energy, or internal kinetic energy (i.e. heat). In fact, some of the energy even takes the form of sound.
 
BobG said:
This is true. Total energy stays constant. It's free to change form from potential to kinetic, or even different types of kinetic energy - the rotational kinetic energy in this example, linear kinetic energy, or internal kinetic energy (i.e. heat). In fact, some of the energy even takes the form of sound.

The thing is the 'lost' energy is exactly 1/2 the total energy !
 
pixel01 said:
The thing is the 'lost' energy is exactly 1/2 the total energy !

It's correct for equal gears (or masses).
 
pixel01 said:
The thing is the 'lost' energy is exactly 1/2 the total energy !

The same thing is true for linear momentum and linear kinetic energy.

If two objects had the same mass, and the first collided with a stationary second object, you'd expect the first object to be stationary while the second moved at the same speed that the first originally had. The fact that they both move at half the speed is a drastically different scenario. Something had to happen for them to stick together.

If you only had one cog on each gear, you'd expect the first gear to transfer momentum to the second and come to a stop; then the second gear to rotate around and transfer momentum back to the first, etc. That would be an interaction that conserved both momentum and kinetic energy.

The reason both are conserved in the one cog example is that you have an opposite and equal reaction every time the gears interact.
 
Last edited:
Since this thread is talking about collisons I would also like to put a question.
In inelastic collisions energy are lost so kinetic Energy isn't conserved. But it is said that momentum is conserved.
Why must it be always the case that objects move after collisions in a way that conserve s the momentum even when the energy needn't be conserved?What I mean, why can't just they come to rest, all of the lost energy coming off as heat!
 
thecritic said:
Since this thread is talking about collisons I would also like to put a question.
In inelastic collisions energy are lost so kinetic Energy isn't conserved. But it is said that momentum is conserved.
Why must it be always the case that objects move after collisions in a way that conserve s the momentum even when the energy needn't be conserved?What I mean, why can't just they come to rest, all of the lost energy coming off as heat!

They can come to rest, but something has to absorb the momentum from the object. For example, a 1000kg car is traveling due East 25 meters per second and eventually comes to rest due to friction and air drag - the Earth absorbs that momentum by spinning faster. Just divide 25000 kg-m by the Earth's moment of inertia ([6 x10^24 kg * 6.4 x 10^6 m]/2 ) and you'll know how much faster the Earth has to spin (in radians per second).

The total energy of the object has to be conserved as well. The only difference is that energy can be converted into different forms (kinetic, potential, etc) and momentum can't.
 

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