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Forces, yanks, and torques

  1. Jul 21, 2010 #1
    So I was thinking physical a while back and I came up with some conceptual conundrums and I was hoping some fine folk can help me sort it out.

    So to change a particle's position, we must apply momentum. For this to be done we must apply a force. and for this, a yank and so on. My question is, how is that we can move the object if we must first change this infinite time derivative of momentum before anything else? and why is force the most important of these? i.e. why are there fundamental forces rather than fundamental yanks?

    Another problem: my brain is telling me that torque defies conservation of energy. If you spin an object with some force near its edge, move closer to the point of pivot and absorb the force from there aren't you getting more force than what you put in?
     
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  3. Jul 21, 2010 #2

    Pythagorean

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    I've always kind of had an issue with this too. There are infinite derivative involved in motion in the classical regime. But we know that this a result of continuity, and continuity doesn't hold in QM (well, not in the same way). So it seems like it's a misleading consequence of classical mechanics, but this is conjecture.

    yes, but energy is still conserved. You have to move the smaller forcer over a greater distance to move the bigger force a small distance. And energy is (to simplify the discussion) Force times distance. It will always work out such that force*distance will be the same value for a fixed pivot point.

    (note this is not the same force*distance as for torque. That distance is distance from the pivot point. We're talking about distance moved. So if you use a lever to move a rock, you have to swing your end down a long ways to move the rock a little ways.) The forces are pretty much the same, but defined in different directions.
     
  4. Jul 21, 2010 #3
    Momentum(p=mv) is something a particle not something that is applied on it. In order to change the particle's position you must you must apply a force on the particle so that you change its momentum. Force is the time rate of change of momentum (F=ma=m(dv/dt)=dp/dt). the bigger the force the faster you can change the particles momentum.
    There isn't such a thing as an infinite time rate of change of momentum, that is there is no infinite force.There also isn't any such thing as an infinite jerk because force and the time rate of force must be finite.
    The force is not the same but the energy is conserved.You apply the outer force on a longer distance then that on which the inner force is applied.Since W=F x ds you will find out that energy is conserved if you do the calculations.
     
  5. Jul 21, 2010 #4

    Pythagorean

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    It's true he's mixing up terminology, but I think what he's really asking about is all the nth derivatives of position as n --> inf.

    In other words, we have position, then:

    1st derivative: velocity (multiply by m, you have momentum)
    2nd derivative: acceleration (multiply m, you have force)
    3rd derivative: jerk (multiply by m, you have yank)
    4th derivative: ????

    Obviously, for you to get from 0 jerk to X jerk, you have to have a change in jerk (otherwise the functions not continuous right?)

    I think he's asking why we don't ever consider the higher derivatives.
     
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