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Find Tension of the rotating rod at a distance x

  1. Oct 8, 2012 #1
    1. The problem statement, all variables and given/known data

    A homogeneous rod with a length L and a mass M rotates with an angular velocity ω in a horizontal plane around an axis passing through its end.Find the tension of the rod at a distance x from its axis of rotation .


    2. Relevant equations



    3. The attempt at a solution

    [tex]T(x)-T(x+dx)=\frac{M}{L}ω^2xdx[/tex]
    [tex]-dT=\frac{M}{L}ω^2xdx[/tex]
    [tex]\int_{T(0)}^{T(x)}dT=-\int_{0}^{x}\frac{M}{L}ω^2xdx[/tex]
    [tex]T(x)-T(0)=-\left[\frac{M}{2L}ω^2x^2\right]_{0}^{x}[/tex]

    Now when x=L,T(L)=0

    Thus,[itex]T(0)=\frac{M}{2L}ω^2L^2[/itex]

    Hence, [itex]T(x)=\frac{M}{2L}ω^2(L^2-x^2)[/itex]

    Kindly check the work if mathematically the steps are correct...
     
  2. jcsd
  3. Oct 8, 2012 #2

    ehild

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    Homework Helper
    Gold Member

    It looks good.

    ehild
     
  4. Oct 8, 2012 #3
    ehild...Thank you very much
     
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