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Pulley wheel rotation question

  1. Dec 19, 2011 #1
    1. The problem statement, all variables and given/known data
    A solid pulley wheel is rotated at a constant velocity for 10 sec's. Find the angular displacement?

    Wo (inital angular velocity) = 6Rad/s
    W (angular Velocity) = 0 Rads/s
    [itex]\alpha[/itex] = 0 (angular acceleration) Rads/s-2
    θ = ? (angular displacement) Rads/s
    t = 10 sec


    2. Relevant equations

    θ=Wo*t+1/2*[itex]\alpha[/itex]*t squared

    θ=(Wo+W)/2)*t


    3. The attempt at a solution

    θ=Wo*t+1/2*[itex]\alpha[/itex]*(t squared)

    displacement θ = 6 * 10 + 1/2 * 0 * t = 60 Rads

    or θ=(6+0)/2)*10 = 30 Rads.

    I cannot tell which one is right as they both should find θ. All I know is that there is an angular acceleration of 0 and 60 is the right answer. Does this mean I have to use an equation with [itex]\alpha[/itex] in it?

    I thought I could use anyone I liked as it found θ.

    Another example is if I decelerate:

    Wo = 6 Rads
    [itex]\alpha[/itex] =-3Rads
    t = 2 sec

    θ=Wo*t+1/2*[itex]\alpha[/itex]*t squared

    displacement θ = 6 * 2 + 1/2 * -3 * (2^2) = 6 Rads

    or θ=(6+0)/2)*2 = 6 Rads.

    Why would this work out or is it just luck? I know the answer to be 6 Rads.

    Thank you for any help in advance. :smile:
     
  2. jcsd
  3. Dec 19, 2011 #2

    Doc Al

    User Avatar

    Staff: Mentor

    OK.
    :confused: I thought the speed was constant? W = 6 rad/s.

    That's fine.

    You are using W = 0, which is incorrect.

    You can use either one. (Of course, all you really need is θ = ωt, since the speed is constant.) But you have to use the right values.

    A little bit of luck. You assumed that the final velocity ω equaled 0 at t = 2 sec. Happens to be true.
     
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