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Rod, conservation of energy and inertia problem! Can someone Explain solution to me?

  1. Nov 12, 2012 #1
    A meter stick is held vertically with one end on the floor and is then allowed
    to fall. Find the speed of the other end just before it hits the floor, assuming that the end
    on the floor does not slip. (Hint: Consider the stick to be a thin rod and use the
    conservation of energy principle)

    Solution on page 6 # HRW 10.63
    http://www.nvcc.edu/home/tstantcheva/231files/hrwch10hw.pdf [Broken]

    Can someone explain the solution to me please??

    I do not understand why PE = 1/2 mgl? where did 1/2 come from?
    How did the first step become ω^(2) equal 3g/L?
    does v = ωL?
    how did ωL = sqrt (3gL)?

    thanks!!
     
    Last edited by a moderator: May 6, 2017
  2. jcsd
  3. Nov 12, 2012 #2

    ehild

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    Re: Rod, conservation of energy and inertia problem! Can someone Explain solution to

    The potential energy of the rod is the sum of the potential energies of its pieces. A little piece at the top has potential energy mgL while the bottom piece has zero PE. The whole potential energy is the same as if all the mass concentrated into the centre of mass, at half the height of the rod.

    ehild.
     
    Last edited by a moderator: May 6, 2017
  4. Nov 12, 2012 #3
    Re: Rod, conservation of energy and inertia problem! Can someone Explain solution to

    so how did 1/2mgL = 1/2(mL^(2)/3)ω^(2) become ω^(2) = 3g/L?
     
  5. Nov 12, 2012 #4

    ehild

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    Re: Rod, conservation of energy and inertia problem! Can someone Explain solution to

    [tex]\frac {1}{2}mgL=\frac {1}{2}\frac{mL^2}{3}\omega ^2[/tex]

    Isolate ω2.

    ehild
     
  6. Nov 12, 2012 #5
    Re: Rod, conservation of energy and inertia problem! Can someone Explain solution to

    im sorry, i dont really understand. how would you isolate ω^2?
     
  7. Nov 12, 2012 #6

    ehild

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    Re: Rod, conservation of energy and inertia problem! Can someone Explain solution to

    Divide both sides of the equation by mL^2, and multiply by 6. What do you get?

    ehild
     
  8. Nov 12, 2012 #7
    Re: Rod, conservation of energy and inertia problem! Can someone Explain solution to

    oooohhhh i got it! ω = sqrt (3g/L)

    so can you explain this part to me

    v = ωL = sqrt (3gL)

    so i know they multiplied L to both side

    but why do we need to find the linear velocity instead of the angular velocity?
     
  9. Nov 12, 2012 #8

    ehild

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    Re: Rod, conservation of energy and inertia problem! Can someone Explain solution to

    You need it because that was the question in the problem. :smile:

    ehild
     
  10. Nov 12, 2012 #9
    Re: Rod, conservation of energy and inertia problem! Can someone Explain solution to

    haha ok thanks for your help!
     
  11. Nov 12, 2012 #10

    ehild

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    Re: Rod, conservation of energy and inertia problem! Can someone Explain solution to

    ω was multiplied by L as the rod rotated about one end, the other end was at distance L from the centre of rotation. L is the radius of the circle the endpoint moves. You know that a point of a roting body at distance R from the centre has the linear velocity Rω.

    ehild
     
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