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Question on angular speed

  1. Apr 8, 2010 #1
    1. The problem statement, all variables and given/known data
    A playground merry-go-round of radius R=2.00m has a moment of intertia [tex]I=250kg.m^2[/tex] and is rotating at 10 rev/min (rpm) about a frictionless vertical axle. Facing the axle, a 25.0kg child hops onto the merry-go-round from the ground and manages to sit down on its edge. What is the new angular speed of the merry-go-round?

    2. Relevant equations
    [tex]\tau=rF[/tex]

    [tex]\tau=I\alpha[/tex]

    [tex]\omega final = \omega initial + \alpha t[/tex]

    3. The attempt at a solution
    I have done this, however my answer is incorrect.

    [tex]\tau=rF[/tex]

    [tex]\tau=2*25a[/tex]

    [tex]\tau=50a[/tex]

    [tex]\tau=Im^2[/tex]

    [tex]50a=250\alpha[/tex]

    [tex]v=\frac{x}{t}[/tex]

    [tex]1.047=\frac{2}{t}[/tex]

    [tex]t=2.094[/tex]

    so....
    [tex]50*{\omega}{t}=250\alpha[/tex]

    [tex]50*\frac{1.047}{2.094}=250\alpha[/tex]

    [tex]\alpha=\frac{25}{250}[/tex]

    [tex]\alpha=0.1[/tex]

    now to find the final angular speed
    [tex]\omega final = \omega initial + \alpha t[/tex]

    [tex]\omega final = 1.047 + 0.1*2.094[/tex]

    [tex]\omega final = 1.2564rad/s[/tex]

    Also a quick question can someone explain to me what is the difference between the
    [tex]\tau=rF[/tex] & [tex]\tau=I\alpha[/tex] equations??
    I'm not quite sure if this is correct; Is the [tex]\tau=rF[/tex] normally used for small rotating mass, and [tex]\tau=I\alpha[/tex] is used for a large rotating body.

    P.S
     
    Last edited: Apr 8, 2010
  2. jcsd
  3. Apr 9, 2010 #2

    tiny-tim

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    Hi Paymemoney! :smile:

    (have a tau: τ and an omega: ω and an alpha: α and try using the X2 tag just above the Reply box :wink:)
    No … "facing the axle" mans that there is no external torque …

    start again, using only conservation of angular momentum. :smile:
    τ = r x F tells you how much the torque is

    τ = Iα tells you what the torque does :wink:

    (and so r x F = Iα tells you what the force does)
     
  4. Apr 9, 2010 #3
    When you are talking about what the torque does, do you mean if it slowing down or accelerating?
     
  5. Apr 9, 2010 #4

    tiny-tim

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    more than that …

    i mean that, just as (linear) force F tells you the (linear) acceleration a (of a body with mass m),

    torque τ tells you the angular acceleration α (of a body with moment of inertia I)

    … they both tell you exactly what the force or torque does to the body :smile:
     
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