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How does a gearbox work?

  1. Dec 9, 2012 #1
    1. The problem statement, all variables and given/known data

    This is related to my other thread https://www.physicsforums.com/showthread.php?t=657677

    Lets suppose i have two gears where the ratio between the rotational speed of the motor and the wheel is:

    Motor/wheel 2:1 first gear
    Motor/wheel 1:1 second gear

    2. Relevant equations

    P=Tω

    3. The attempt at a solution

    Now i guess that in the first gear following holds

    [tex]P_m=ω_m*T_m=ω_w*T_w=P_w=2*ω_w*\frac{T_w}{2}[/tex]

    That means that the mechanical energy on the rotational axis is the same on both sides of the gearbox?

    Is that correct?
     
  2. jcsd
  3. Dec 9, 2012 #2

    CWatters

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    Science Advisor
    Homework Helper

    Yes. If you ignore losses in the gearbox then a gearbox doesn't change the power. It just trades torque and angular velocity.

    You can also think of it in terms of the law of conservation of energy. A gearbox can't store or create energy so what goes in must come out (and at the same rate = power).
     
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