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Derivation to find unknowns

  1. Mar 4, 2007 #1
    1. The problem statement, all variables and given/known data

    At t=0 the current to a dc electric motor is reversed, resulting in an angular displacement of the motor shaft given by theta (t) = ( A)t-( B)t^{2}-( C)t^{3}

    At what time is the angular velocity of the motor shaft zero?

    2. Relevant equations

    quadratic

    3. The attempt at a solution

    I continue to be very confused by this question. I thought all I need to do was take the derivative with respect to time and then plug those coefficients into the quadratic equation.
    So I get:

    (2B(+/-)((4B^2+12AC)^.5))/2A
     
  2. jcsd
  3. Mar 4, 2007 #2

    arildno

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    1. You have interchanged the roles of A and -3C here, so your expression is not correct.
    2. Which of the times you get out is not physically meaningful?
     
  4. Mar 5, 2007 #3
    Well I got that part figured out but I can't get the next part.

    1.
    How many revolutions does the motor shaft turn through between the time when the current is reversed and the instant when the angular velocity is zero?
    2.
    Deltatheta=.5(w+w0)t
    revolution=(1/2pi)radians
    3.
    Since the final velocity is zero:
    deltatheta=.5tw0
    revolutions=(.5tw0)/(2pi)
    w0=A
    so;

    =.5tA/2pi (where t is the time when angular velocity =0)


    Thanks,
    Nate
     
  5. May 24, 2008 #4
    Question: How many revolutions does the motor shaft turn through between the time when the current is reversed and the instant when the angular velocity is zero?

    Ans: Well, assuming that you found the time t when the angular velocity is zero, all you need to find out here is the revolutions between zero and that time t.

    Plug in the time t into the angular displacement equation that you have, and you should get something in radian measure.

    Then, the next thing that tricked me out was that I didn't know the conversion from radian to revolutions. (a simple thing, I know, but I overlooked it)

    1 revolution = 2*pi radians.

    Convert, and viola you have how many revolutions.
     
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