Angular Momentum Conservation in Gear Interactions

In summary, when a rotating gear with an upward-pointing angular momentum vector meshes with a stationary gear of equal radius and moment of inertia, the angular momentum of the second gear will be pointing down due to its opposite rotation direction. This results in a non-conservation of angular momentum since the total angular momentum of the system, including the axle of the gears, will sum to zero after the collision.
  • #1
george heck
1
0
Lets say one gear is rotating with some angular velocity and its angular momentum vector is pointing up.
A second gear (not rotating) is then allowed to mesh with the first. The second gear has the same radius and moment of inertia as the first.
Is not the angular momentum vector of the second gear pointing down since it rotates opposite to the first?
and if so, how is it that angular momentum is conserved as one gear will have positive and the other negative
angualar momentum - thus summing to zero, (after the "collision")?

thanks
 
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  • #2
Hint : It isn't conserved . Look at the axle of the gears . Are they part of your system ?
 

Related to Angular Momentum Conservation in Gear Interactions

1. What is angular momentum?

Angular momentum is a measure of an object's rotational motion. It is defined as the product of an object's moment of inertia and its angular velocity.

2. How do gears affect angular momentum?

Gears can affect angular momentum by changing the moment of inertia and angular velocity of a system. When gears are connected, their rotational motion is linked, causing a transfer of angular momentum between them.

3. What is the relationship between gear size and angular momentum?

The moment of inertia of a gear is directly proportional to its size. This means that a larger gear will have a greater moment of inertia and therefore, a greater angular momentum.

4. How do you calculate angular momentum with gears?

To calculate the angular momentum of a system with gears, you can use the formula L = Iω, where L is the angular momentum, I is the moment of inertia, and ω is the angular velocity. You will need to calculate the moment of inertia for each gear and then determine the angular velocity of the system.

5. Can angular momentum be conserved in a system with gears?

Yes, angular momentum can be conserved in a system with gears as long as there is no external torque acting on the system. This is known as the law of conservation of angular momentum and it states that the total angular momentum of a system remains constant unless an external torque is applied.

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