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Angular Velocity Graph

  1. Jun 18, 2012 #1
    1. The problem statement, all variables and given/known data
    The graph shows the angular velocity of a rotating wheel as a function of time.
    https://online-s.physics.uiuc.edu/cgi/courses/shell/common/showme.pl?cc/DuPage/Phys1201/summer/homework/Ch-10-Rotation/ang_vel_graph/omega_vs_t-2.jpg [Broken]

    What is the angular displacement of the wheel at t = 2.4 sec?

    2. Relevant equations
    ωf=ωi+αt

    θ=θ0+ωit+1/2αt2


    3. The attempt at a solution
    I first try to find the acceleration it takes from initial angular velocity to move to t=2.4s
    -6=-9+a(2.4)=1.25
    α=1.25

    so assuming θ0=0

    θ=-9(2.4)+1/2(1.25)(2.4)2
    θ=-18?
     
    Last edited by a moderator: May 6, 2017
  2. jcsd
  3. Jun 18, 2012 #2
    any ideas? i also tried W=θ/t
     
  4. Jun 18, 2012 #3
    what about bxh/2= 2.4*-6/2=-7.2 since the θ is the area is between above the line and the horitzonal x
     
  5. Jun 18, 2012 #4
    Your calculated angular acceleration is wrong. The angular velocity at time zero is -9 rad/s, and it is zero at time 6 seconds. So it increases by 9 rad/s over a time interval of 6 seconds.
     
    Last edited by a moderator: May 6, 2017
  6. Jun 18, 2012 #5
    Thanks,
    but shouldnt my final angular velocity be -6 since its asking for the displacemente at 2.4s?
     
  7. Jun 19, 2012 #6
    It is a constant acceleration. Which means Δv/Δt is constant. You can take any points as values.
    The problem is that you are taking velocity at time of 2.4 secs.
    You can only get approximate value of v at 2.4 sec from the graph.

    Rather than taking value of velocity at 2.4sec, why not use other values that easy and accurate to calculate. It does not matter where you get your Δv and Δt since it is a linear function.
     
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