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Bowling Bowl - Center of mass - Friction - Angular Acceleration/Velocity

  1. Jun 21, 2009 #1
    1. The problem statement, all variables and given/known data

    A bowling ball with Mass M and Radius R is thrown down an alley so that the balls center of mass has an initial horizontal velocity of Vo and the ball is not rotating. Kinetic friction force is f^k. Find:

    a) an expression for the acceleration and velocity of the ball's center of mass (a) as a function of time (t)
    b) in terms of M, R, Vo, and f^k, write down an expression for the angular acceleration and angular velocity as a function of time
    c) at some time t^r, the ball will stop slipping on the alley and will start to roll w/out slipping. What are the conditions for this to happen
    d) using these conditions in part (c), find the time t^r at which the ball starts to roll w/out slipping (in terms of M, R, Vo and f^k


    3. The attempt at a solution

    a) a=Vo/dt ?
    b) angular acc = Torque/I
    Torque = R x F
    F= M X A
    I = 2/3 x M x R^2 ?
    c) v= R x w (ang velocity)
    d) ???

    Thanks so much for the help!!
     
  2. jcsd
  3. Jun 21, 2009 #2

    Doc Al

    User Avatar

    Staff: Mentor

    Use Newton's 2nd law to find the acceleration, then apply standard kinematic formulas.
    OK. Do the same thing as in part a, only for rotation.
    That's for a spherical shell--a bowling ball is solid.
    Good--that's the condition for rolling without slipping.

    The basic idea is this. The friction force does two things: It slows the translational speed as it raises the angular speed. Solve for the point at which those speeds meet the condition for rolling without slipping.
     
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