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Motion In A Circle

  1. Nov 5, 2007 #1
    A boy ties a 500kg rock to a 1.0m long string and swings it around his head in a horizontal circle. At what angular velocity, in rpm, does the string tilt down at a 10 degree angle?

    sintheta = mg / T

    sin10 = 0.5kg(9.8m/s^2) / T

    T = 4.9N / sin10

    T = 28.22N

    THEN...

    v = SqRt [(rTcostheta) / m] ---> However the radius of the circle is not the length (L) so, r = Lcostheta

    v = SqRt [(LTcos^2 theta) / m]

    v = SqRt [(1.0m)(28.22N)(cos10^2) / 0.5kg]

    v = 7.4m/s

    FINALLY...

    OMEGA = v / r
    = v / Lcostheta

    7.4rad / 1sec x 1rev / (2pi)rad x 60sec / 1 min --> rad and sec cancel out, leaving...

    = 70.7 rpm


    This was my initial attempt to the problem but I am not sure if everything is correct?
     
  2. jcsd
  3. Nov 5, 2007 #2

    Astronuc

    User Avatar

    Staff: Mentor

    Looks fine through v = 7.4 m/s, but then look at [itex]\omega[/itex] = v/r = v/(L cos (10°).

    cos 10° = 0.985, so [itex]\omega[/itex] = (7.4 m/s)/(0.985 m) = 7.51 rad/s

    The rest is correct in form.
     
  4. Nov 5, 2007 #3
    Thanks for the correction!
     
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