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Find the force at the middle point of the rod

  1. Jan 22, 2008 #1
    1. The problem statement, all variables and given/known data

    A rod of length L,mass m is clamped at one end to a wall.The rod is rotated with angular velocity @ (omega say).Find the force at the middle point of the rod.

    2. Relevant equations

    Force = ma
    Centripetal force = mw^2r

    3. The attempt at a solution

    I think there is some integration in this but I cant seem to make out what all forces are applied at the mid point.
  2. jcsd
  3. Jan 22, 2008 #2

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    When a rod is hanging from one end, the bottom half of the rod will pull down on the mid point, while the upper half will not exert any force at that point.

    Here, too, the outer part is exerting a centrifugal force outward at the mid point. Assume some linear mass density of the rod, and then integrate the force from L/2 to L.

    (If dx is the elementary length at a dist x, then its mass dm = rho*dx, and you know its w in terms of x.)
    Last edited: Jan 22, 2008
  4. Jan 22, 2008 #3
    Why is that?I mean why doesnt the inside part exert force?
    Last edited: Jan 22, 2008
  5. Jan 22, 2008 #4

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    Refer to the hanging rod example. The weight of the lower half is supported by the tension at the mid-point, while the weight of the upper half is not. But at the topmost point, the whole weight of the rod is supported.

    Here too, the centrifugal force acts outward and away from the centre. It's a very similar scenario. The part which is "outer" to the mid-point pulls outward at the mid-point. The part which is inward to the mid-point is already supported by the force at the pivot, like the topmost point of the hanging rod.
  6. Jan 23, 2008 #5
    All right thank you.
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