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Conservation of angular momentum & linear momentum

  1. Feb 7, 2016 #1
    Two things I'd like to discuss:

    1. The conservation of angular momentum. If you have two discs rotating on the same fixed rigid axis, will these nullify each other? I.e. Create no net angular momentum?

    2. How / is it possible to convert angular momentum to linear momentum in the sense to be able to find the an equivalent linear displacement that could be produced?
  2. jcsd
  3. Feb 7, 2016 #2

    Buzz Bloom

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    Hi Sirsh:

    1. Assuming the discs are rotating in opposite directions, yes.

    I do not understand this question. Conservation laws do not allow getting rid of angular momentum as an exchange for adding linear momentum. However, some devices might be engineered to exchange moving angular momentum from one part of a system to another with moving some linear momentum from one part to another. As to how, I can't help you since I don't have the engineering skill.

    Hope this is helpful.

  4. Feb 7, 2016 #3
    Sorry Buzz, I should have tried to explain it better.

    I want to know if you can counteract linear momentum with angular momentum, for example if you were pushing a cart on frictionless wheels in one direction, but on this cart had a large wheel that was heavy enough to create a sufficient angular momentum in the opposite direction of the carts travel, would it influence the direction it is travelling? as in, would it be possible to stop the carts motion with this big wheel?
  5. Feb 8, 2016 #4


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    The apart from the mass of the disc adding to the linear momentum of the cart, the gyroscopic effect of the spinning disc is the only element that will effect the motion of the cart. If the cart were to continue in a straight line through free space, the gyroscopic forces would have only a minor effect over a short time period; however, on our spinning and orbiting planet, unless the disc's axis is aligned with the central axis of the earth and the travel path of the cart is perpendicular to that axis, over an hour or so of travel time, it will eventually either turn the cart, tilt it toward one side or some combination of both. Given an even longer time period, the perturbation of our planet's axis and the rotation of our planet about the sun will result in similar effects.
  6. Feb 8, 2016 #5

    Buzz Bloom

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    Hi @Sirsh:

    When I first saw JBA's post, I thought it was a complete answer, but I have thought about it some more, and now I am not so sure.

    I visualize the cart as having two axles, front and back, with two wheels on each axle. In the center of the cart I visualize two parallel supports for a third axle parallel with the other two, and fifth wheel on this axle in the exact center of the cart's platform. The cart is on level ground, and I think it simplifies to think of the wheels on straight tracks. Some people push the cart which gets it moving, with the wheels turning as it moves. If we ignore friction slowing the cart down, it will continue indefinitely at the speed it has when the people stopped pushing it.

    Now there is a crank on both sides of the fifth wheel. I imagine two people standing on the platform of the cart turning the crank so that it starts to rotate in the opposite direction of the other four wheels. As the two people continue to turn the crank faster and faster, the fifth wheel turns faster and faster. Does this cause the cart to slow down?

    At this point I am thinking that the feet of the people turning the crank are exerting a force on the platform in the opposite direction than the cart's motion. If the fifth axle was not allowed to rotate, this would have no affect on the cart's speed, because there would also be an equal force on the stationary crank so there would be no net force on the cart. But maybe there is a possibility that when the fifth wheel rotates there is less linear force on the fifth axle than the force the feet apply to the deck, because much of the force on the crank results in energy added to the fifth wheel rather then balancing the force of the feet. In that case I think this might possibly slow the cart. However, the slowing is not due to the fifth wheel spinning. That is side effect of converting the linear force of the feet into torque on the wheel.

  7. Feb 8, 2016 #6
    Your description of the scenario is very similar to the way I was thinking albeit on a much larger scale.

    So you're saying there is absolutely no ability for the wheel to exhibit any inhibition to the positive linear motion of the cart?

    Even in a hypothetical situation where the wheel on the cart was say 1000kg and rotating at 6000 RPM, and the cart being only 10kg but structurally rigid/stable is traveling at 1m/s?
  8. Feb 8, 2016 #7


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    The rotational momentum is circular therefore if it is backward on the top then it is forward on the bottom so the linear horizontal effect (if there were any) would cancel.
  9. Feb 8, 2016 #8
    That's true. So I guess, the cart would roll while the wheel goes berserk.

    The aim of this thought process is for something I'm working on (stuck on actually) which needs a mechanism that will allow a retardant to positive linear motion on a low coefficient of friction surface, so when positive motion is applied, something needs to supply negative linear motion. But I cannot figure out a mechanism that will do this that isn't electronic or always providing negative linear motion. :oldconfused:
  10. Feb 9, 2016 #9


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    Basically, it appears you need an equal counteracting force to the forward driving force. Why is the use of an electric source unacceptable? What is the source of the forward motion creating force? What "unacceptable' method(s) have you envisioned, Please describe your problem in a bit more detail.
  11. Feb 9, 2016 #10
    I'm trying to build a mechanistic pedalling machine for myself, but the ones I've built move forwards when I pedal due to slippage on carpet (it has 4 feet). I am currently looking into ways to increase the frictional force between the carpet and some other material (feet of my machine that are of my selection), but I thought there may be a way to create an opposite and equal force to my pedalling action, hence the reason for trying to use a reverse flywheel.

    I don't want it to have to be connected to a power outlet, but there is a possibility that I connect a small DC generator to the crankshaft through gearing if absolutely required, if it will allow the machine to not move forwards.

    I've done research on the forces that are generated due to the pedalling forces through peer-reviewed papers on actual cyclists and they come to be in the range of 200-300 N when at a crank angle of approximately 110 degrees (0 degrees is TDC of the crankshaft).
  12. Feb 10, 2016 #11


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    In free space you can't convert rotation to linear motion because that would breech conservation of momentum and amount to a reaction less rocket. I suspect you machine moves due to....


    Flywheels and gyroscopes don't produce thrust only torque.
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