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Torque v. Time Graph -- Find angular velocity

  1. Dec 2, 2014 #1
    1. The problem statement, all variables and given/known data
    An object whose moment of inertia is 3.00kgm2experiences the torque shown in the figure (Figure 1) . What is the object's angular velocity at 2.80s ? Assume it starts from rest.

    2. Relevant equations
    Torque=angular acceleration * moment of inertia
    angular velocity = angular acceleration * change in time

    3. The attempt at a solution
    From what I can understand of the problem, the angular acceleration is 0 (because torque is 0), but angular velocity is not zero so it must be some constant. However, I'm struggling how to figure out what that is.
  2. jcsd
  3. Dec 2, 2014 #2


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    The angular acceleration is the time derivative of angular velocity, so Idω/dt = τ. You get the angular velocity at a given instant by integrating the angular acceleration with respect to time.
    Last edited: Dec 2, 2014
  4. Dec 2, 2014 #3
    Could you please ellaborate in context of this problem? I just can't find any examples of problems like this so I just need a little bit more explaination
  5. Dec 2, 2014 #4
    By integrating angular acceleration with respect to time, I get w= at + c (constant). a= 0 t=2.8s but how do I determine the constant? Which will equal the velocity
  6. Dec 2, 2014 #5


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    Use definite integral.
    ##\frac{d\omega}{dt }= \frac {\tau (t)}{I}##. Integrate from t=0 to t=2.8 s. You have to do the integral separately in all the three time intervals and add them
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