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Angular velocity of a ball

  1. Dec 4, 2011 #1
    1. The problem statement, all variables and given/known data

    A ball of mass 0.5 kg is attached to the end of a string of length 0.5 m. The ball rotates in a horizontal circular path about a vertical axis. The maximum tension on the string cannot exceed 324 N. What is the maximum possible angular velocity of the ball in rad/s ?

    2. Relevant equations

    2/r = tension on the string.

    3. The attempt at a solution

    I don't think the equation is correct. It should be v and not ω. However, what I wanted to do was to equate the centripetal force with the maximum force on the string. I got the answer as 18, which is not correct. I tried to use mg instead of m but that was wrong too.

    The correct equation is T = mg + mLω2, but why?

    Why can I not use the centripetal force equation here?
  2. jcsd
  3. Dec 4, 2011 #2
    The centripetal force is given by mrω^2 or mv^2/r.
    If this ball is on a table in a horizontal circle the r = 0.5m.
    If the string is being held in the hand then there will be an angle ∅ to the horizontal.
    You will then need to resolve the tension in the string into a vertical component to balance the weight of the ball and a horizontal component to provide the resultant centripetal force.
    Hope this helps
  4. Dec 4, 2011 #3
    Are sure it is in a HORIZONTAL circle !!!!!
    The equation you have given as correct is for a VERTICAL circle !!!
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