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Homework Help: Dynamics: planar kinetics of a rigid body (impulse and momentum)

  1. Jan 8, 2010 #1
    1. The problem statement, all variables and given/known data
    http://img340.imageshack.us/img340/7379/87835960.png [Broken]
    [itex]r_{i}=.3 m \text{ and } r_{o}=.9 m[/itex]
    The spool has a weight of 300N and a radius of gyration [itex]k_{O}[/itex] = .45 m. A cord is wrapped around its inner hub and the end subjected to a horizontal force P = 50N. Determine the spool's angular velocity in 4seconds starting from rest. Assume the spool rolls without slipping.


    2. Relevant equations
    [itex]\int_{0}^{t}{P\cdot r_{i}}{dt} = mv_{O}r_{i} + I_{O}\omega[/itex]


    3. The attempt at a solution
    [itex]\left \{ \begin{matrix}\int_{0}^{4}{50 \cdot 0.3}{dt} = \frac{300}{9.81}\cdot v_{O}\cdot0.9 + \frac{300}{9.81}\cdot 0.45^{2} \cdot \omega\\v_{O}=0.9\omega\end{matrix}[/itex]
    Solving the two equations i get [itex]\omega = 1.94 \text{rad/s}[/itex]

    The book provides the solution as follows
    [itex]\left \{ \begin{matrix}
    50(0.9 - 0.3)4 = \frac{300}{9.81}v_{O}\cdot 0.9+\frac{300}{9.81}\cdot.45^{2}\omega \\
    v_{O}=\omega\cdot0.9 \end{matrix}[/itex]
    I dont get why the book does .9 - .3 for its radius, i thought it was around point O?
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Jan 8, 2010 #2

    tiny-tim

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    Hi silentwf! :smile:

    (have an omega: ω and an integral: ∫ :wink:)
    [STRIKE]You can't take moments about the centre of mass (O) when it is accelerating.

    But you can always take moments about the centre of rotation (A).[/STRIKE]

    If you take moments about the centre of mass (O), you need to take the torque of the friction force at A into account.

    To avoid that, use A instead of O, so that the friction torque is zero.

    So all you need is the torque of P about A, for which the distance is 0.6 :wink:
     
    Last edited: Jan 8, 2010
  4. Jan 8, 2010 #3

    tiny-tim

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    oops!

    I've changed my mind …

    the conclusion of my last post is still correct (that you must take moments about A, not about O), but the reasoning wasn't, so I've edited it. :redface:
     
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