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Rotational Dynamics and string Tension

  1. May 24, 2014 #1
    1. The problem statement, all variables and given/known data

    A light string is wrapped around a solid cylinder and a 300g mass hangs from the free end of the string. when released, the mass falls a distance of 54cm in 3.0s.
    a) Calculate the tension in the string.
    b) Calculate the mass of the cylinder.

    2. Relevant equations

    y=y0 + v0t + 1/2at^2
    I=mr^2
    α=a/r
    T-mg=ma
    F=ma
    τ=Iα
    τ=rF

    3. The attempt at a solution

    a) y=y0 + v0t + 1/2at^2
    0.54m = (0.5)a(3s^2)
    a=0.12m/s^2

    T-mg=ma
    T-(0.3kg)(9.8m/s^2) = (0.3kg)(0.12m/s^2)
    T=2.979N

    b) τ=Iα
    τ=mr^2α
    Fr=mr^2α
    F=mrα

    I'm not sure if thats right for a), I feel like I'm missing something.... :frown:
    I'm very confused for b). I have been playing around with the equations, as you can see above, but I keep going in circles and I feel like I don't have enough information. Thanks in advanced for any help!!
     
  2. jcsd
  3. May 24, 2014 #2

    SammyS

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    Hello Juniper7. Welcome to PF !

    First of all, there is at least one missing detail. Is the cylinder free to rotate on its axis ?

    The form of the moment of inertial you have, I = mr2 is for a hollow cylinder, not a solid one.

    You use both F and T, somewhat interchangeably.


    Draw 2 free body diagrams; one for the hanging mass, and one for the cylinder?

    Doing these things should help take the guesswork out of what equations to employ.
     
  4. May 24, 2014 #3
    Oh, ok. I think I have it now. The cylinder is freely rotating. Thanks!
     
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