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Minimum Angular Velocity Problem

  1. Dec 9, 2013 #1
    First off, I want to apologize for posting more than one question. I just discovered this site, so I wanted to check my work while I am able to. Thank you again.

    1. The problem statement, all variables and given/known data

    A massless rope of length L = 1 m is swung in the vertical plane, with a bob of mass m = 1 kg attached to its end.

    (a) Calculate the minimum angular velocity ωmin that the bob of must have to keep the rope taut at every point in the trajectory.

    (b) Assume now that the bob starts from the lowest position (θ = 0) at rest, and the angular velocity follows

    ω = 2 x t rad s-1

    Calculate the time at which the bob reaches the top position.

    2. Relevant equations

    Fc = (m)(v2/R)

    R = L

    Fc = (m)(v2/L)

    v = (L)(ω)

    Fc = (m)((Lω)2/L)

    Fc = (m)((L)2(ω)2/L)

    Fc = (m)((L)(ω)2)

    At the top of the circle:
    (m)((L)(ω)2) = (m)(g)

    ((L)(ω)2) = (g)

    ω = √(g/L)

    3. The attempt at a solution

    (a) ω = √(10/1)
    ω = 3.16 rad/s

    Did I go about doing this correctly?

    (b) I wasn't quite sure on how to start this part. I know that 1 radian is half a revolution. Therefore, to reach the top from the bottom (half a revolution), the time it takes t would have to be how long it takes to go one radian. Plugging in .5 yields 1 in the equation given in part b, but I don't know if this is correct.
     
    Last edited: Dec 9, 2013
  2. jcsd
  3. Dec 9, 2013 #2
    1 radian does not equal half of one revolution.

    ∏ radians equals one half of one revolution.

    Beyond that point, what exactly is the question in part b?
     
  4. Dec 9, 2013 #3
    Oh, sorry, I forgot to add it, it's there now.
     
  5. Dec 9, 2013 #4
    Hmmm, I'm not the greatest with pendulum stuff.

    Perhaps, since you know that;

    2 x t rad s-1 = ω = √(g/L)

    You might be able to get a result from that?
     
  6. Dec 9, 2013 #5
    So perhaps;

    2 x t rad/s = 3.16 rad/s
    t = 1.58 seconds?

    Does that make sense?
     
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