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I Question of Leverage in Rotating Mechanisms

  1. Jun 18, 2017 #1

    ejn

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    New to physics, so looking to this board for more knowledgeable and experienced help in trying to understand the potential effect of leverage in circular motion.

    Imagine two disks, A and B, each 1 foot in diameter. Each disk is permanently attached at its center to a vertical shaft which spins freely in any direction. Assume near-zero friction between the shaft and the bearings that hold it in place vertically. Below each disk, and also attached at their centers to the shafts, are two other smaller disks. Disk a is 6 inches in diameter. Disk b is 3 inches in diameter. Wrapped around the edges of the two smaller disks a and b is a belt, which cannot slip, forcing both sets of disks to rotate in a clockwise manner. Thus, when disk A completes one full rotation, disk B will have completed two full rotations. (At least I think that is what will happen.)

    Imagine now two momentary/pulse forces of equal strength, emanating from the edges of larger disks A and B, and directed against each other at a 45 degree angle to a line that intersects the center of both vertical shafts. The effect of these two forces is that the disks will rotate away from each other at the point of the two forces, both in a clockwise direction. (Clockwise or counterclockwise doesn't matter to my question...just wanting us all to be on the same page.)

    Question: Does the existence of the smaller disks connected by the belt either increase or decrease the effect of the forces upon each other? For example, is the force from disk A (with the larger of the two smaller disks) effectively increased over the force from disk B? If so, by how much? Or would the opposing forces need to emanate from the smaller disks here for there to be any mechanical advantage of force?

    If we recompose the problem to be one where the opposing forces are still emanating from larger disks A and B, but disk A is 1 foot in diameter, disk B is 2 feet in diameter, and smaller disks a and b are both six inches in diameter and connected by the belt, which disk has the mechanical advantage, A or B?
    ejn2017
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  2. jcsd
  3. Jun 18, 2017 #2
    Isn't this an internal contradiction? In the first line, both disks are 1 ft in diameter, but later they are 6" and 3" in diameter. How can this be?
     
  4. Jun 18, 2017 #3

    ejn

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    Note the distinction of using capital letters A and B when referring to the larger disks and lowercase a and b when referring to the smaller disks.
     
  5. Jun 18, 2017 #4
    Well, this is where a diagram would help a lot to avoid any confusion.
     
  6. Jun 20, 2017 #5

    CWatters

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    I think a diagram is essential.
     
  7. Jun 20, 2017 #6

    ejn

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    OK, I've uploaded a diagram. Given that, please ignore my original question posted above and focus on the two questions in the diagram (just in case there are inconsistencies between the original post and the diagram).
     

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  8. Jun 21, 2017 #7

    CWatters

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    F1 and F2 both accelerate the discs in the anticlockwise direction.

    The general equation.....

    Torque = moment of inertia * angular acceleration

    can be modified to take into account the gearing of the pulleys.
     
  9. Jun 21, 2017 #8

    A.T.

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    What do you mean by "which force has the mechanical advantage"? They are both of same magnitude according to the box in the middle. And they both oppose the indicated CW rotation.
     
  10. Jun 21, 2017 #9

    jbriggs444

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    One could ask: "Which way would the disks rotate under the tension of a rubber band between the indicated points".

    And one could answer by looking at how those two points draw together or spread apart as the linked mechanism is rotated.
     
  11. Jun 21, 2017 #10

    A.T.

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    Counter clockwise. But the description sounds like these are friction forces, assuming the indicated clockwise direction.

    I still don't understand the question.
     
  12. Jun 22, 2017 #11

    A.T.

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    Or for example:

    - Which part of the belt will be under (higher) tension, when the big disks come into contact, while rotating as indicated?

    - What is the direction of energy flow via the belt?
     
    Last edited: Jun 22, 2017
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