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Angular acceleration of an axle

  1. Oct 18, 2006 #1
    A disk with a radial line painted on it is mounted on an axle perpendicular to it and running through its center. It is initially at rest, with the line at theta 0 = -90°. The disk then undergoes constant angular acceleration. After accelerating for 3.1 s, the reference line has been moved part way around the circle (in a counterclockwise direction) to theta f = 130°.

    Given this information, what is the angular speed of the disk after it has traveled one complete revolution (when it returns to its original position at -90°)?


    [​IMG]

    here is my work:

    360-130=230 degrees.

    130(pi/180)=2.26 radians
    230(pi/180)=4.014 radians

    theta=Wot + at^2 /2

    4.014 = a (9.61)/2
    9.61a = 8.09

    a1=.84 radians

    2.26/3.1 = .73 rad/s

    a2=.73 radians

    .84 + .73 = 1.57 rad/s

    I found the acceleration of the first 130 degrees; the acceleration of the last 230 degrees, added them, but my answer is wrong. any idea why?
     
  2. jcsd
  3. Oct 18, 2006 #2

    Doc Al

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    Staff: Mentor

    The disk moves from -90 degrees to 130 degrees: 130 - (-90) = 220 degrees in the time given. Find the angular acceleration using that data.
     
  4. Oct 22, 2006 #3
    I've calculated 220 (pi/180) = 3.8397 rad/s

    3.8397 rad = (a(9.61))/2
    a = .79911 rad/s

    So I have calculated the constant acceleration; how do I find the speed after one revolution?
     
  5. Oct 23, 2006 #4

    Doc Al

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    Staff: Mentor

    Good. (But the units are rad/s^2.)

    It's just another kinematics problem. What other kinematic relationships are you familiar with? (One useful one relates velocity and distance--or angular velocity and angle--directly.) What can you determine from the given data?
     
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