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Conservationof energy and angular speed

  1. Oct 20, 2008 #1
    A small 13.0-g bug stands at one end of a thin uniform bar that is initially at rest on a smooth horizontal table. The other end of the bar pivots about a nail driven into the table and can rotate freely, without friction. The bar has mass 70.0 g and is 90 cm in length. The bug jumps off in the horizontal direction, perpendicular to the bar, with a speed of 25.0 cm/s relative to the table.

    1. The problem statement, all variables and given/known data
    What is the angular speed of the bar just after the frisky insect leaps?
    mass of bug = .013kg
    mass of bar = .070kg
    length of bar = 0.9m
    final velocity of bug = 0.25 m/s
    initial velocity of bug = 0
    initial velocity of bar = 0

    2. Relevant equations
    I = (1/3)ML^2
    K(bug) = (1/2)mV^2
    K(bar) = (1/2)Iw
    Sum of the energy before = sum of the energy after

    3. The attempt at a solution
    0 = K(bug) + K(bar)
    0 = (1/2)mV^2 + (1/2)Iw
    0 = (1/2)mV^2 + (1/2)(1/3)ML^2w
    w = -[mV^2]/[(1/3)ML^2]

    but that doesn't come out with the correct answer

    where w is the lowercase omega standing for angular velocity
     
    Last edited: Oct 20, 2008
  2. jcsd
  3. Oct 20, 2008 #2

    hage567

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    Just quickly looking at this, I notice you left the square off the omega in your equation for rotational kinetic energy. It should be K(bar) = 0.5Iw^2.
     
  4. Oct 20, 2008 #3
    Ya, i noticed that a little bit ago, and when I put in the square... This is from a problem in the book with different values, but using the values in the book, my answer still does not agree with the answer in the book. If i did everything right, maybe the answer in the book is wrong...it could happen lol.
     
  5. Oct 21, 2008 #4
    Well, the final answer turned out to be 0.155 rad/s, but I'm not sure why
     
  6. Oct 21, 2008 #5

    hage567

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    So this is the book's answer?
     
  7. Oct 22, 2008 #6
    yes, using these values, that is the answer
     
  8. Oct 22, 2008 #7

    hage567

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    Was the book using conservation of energy in the example? I would use conservation of angular momentum about the pivot point for this problem.
     
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