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Vertical circular motion

  1. Jan 3, 2009 #1
    1. The problem statement, all variables and given/known data

    A 0.4 kg object rotates in a vertical circle at the end of a 0.5 m string. What is the tension of the string at the bottom if the angular velocity there is 8.0 rad/s?

    2. Relevant equations

    centripetal acceleration = R*w^2
    weight = mg
    R = radius of circle
    w = angular velocity

    3. The attempt at a solution

    centripetal acceleration = (0.5 m)(8.0/s)^2 = 32 m/s^2
    total (centripetal) force = (0.4 kg)(32 m/s^2) = 12.8 N (upwards)
    weight = (0.4 kg)(9.8 m/s^2) = 3.9 N (downwards)
    Upwards forces and accelerations will be considered positive, downwards ones negative.
    total (centripetal) force = string tension - weight
    12.8 N = string tension - 3.9 N
    string tension = 12.8 N + 3.9 N = 16.7 N
    In general terms:
    string tension = mg + mRw^2

    Unfortunately, the "official" solution is 13 N.
    Am I wrong, or are my course materials wrong?
    Will I be equally puzzled if I try to take the AP Physics B exam?
  2. jcsd
  3. Jan 3, 2009 #2


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    Science Advisor
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    Gold Member

    Kyriam, welcome to PF! Your answer and method is good! I think you'll do OK in the exam.
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