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Rotational motion- steam engine

  1. Mar 7, 2007 #1
    1. The problem statement, all variables and given/known data

    The flywheel of a steam engine begins to rotate from rest with a constant angular acceleration of 1.35 rad/s^2. It accelerates for 33.1 s, then maintains a constant angular velocity. Calculate the total angle through which the wheel has turned 47.5 s after it begins rotating.

    2. Relevant equations

    1. w=wi +alpha(time)

    2. theta - theta(initial) = 1/2(w +wi)t

    3. The attempt at a solution
    I have attempted this problem several times and keep getting the answer wrong!!! (note: I do not know the correct answer for this particular problem)

    First I used equation 1 to find the constant angular velocity. Then, since I know that constant velocity means zero acceleration, I used equation 2 to find the total angle. What am I doing wrong? Please help!:confused:
     
  2. jcsd
  3. Mar 7, 2007 #2

    Andrew Mason

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    Science Advisor
    Homework Helper

    It would help to graph the angular speed as a function of time. The area under the graph is what you are trying to calculate.

    If it starts at [itex]\omega = 0[/itex] then [itex]\omega = \alpha t[/itex] and:

    [tex]\theta_1 = \frac{1}{2}\alpha t_1^2[/tex] (angle after 33.1 seconds)

    [tex]\theta_2 = \alpha(t_1) (t_f - t_1)[/tex] (increase in angle to t= 47.5 seconds)

    which is essentially what you have already figured out. Just add those two equations to get [itex]\theta = \theta_1 + \theta_2 [/itex] and solve.

    AM
     
  4. Mar 7, 2007 #3

    Mentz114

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    Gold Member

    There are 2 phases - 33.1s of acceleration and 14.4s of constant velocity.
    You must calculate the number of turns for each phase and add them.
    Adapt the well known relations

    distance = 1/2*acc*time^2
    distance = velocity*time

    to the angular case.
     
  5. Mar 7, 2007 #4
    thank you very much, I got the answer correctly. :smile:
     
  6. Nov 7, 2009 #5
    I am actually using θ1= ½ αt12 and θ2=α (t1)(tf-t1) and adding both angles together but I am not getting the answer right??

    thanks
     
    Last edited: Nov 7, 2009
  7. Nov 7, 2009 #6
    aha, the answer was in radians, not degrees
     
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