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Rotational Motion

  1. Jul 4, 2015 #1
    1. The problem statement, all variables and given/known data

    An object of rotational inertia I is initially at rest. A torque is then applied to the object, causing it to begin rotating. The torque is applied for only one-quarter of a revolution, during which time its magnitude is given by \tau =Acos\Theta , where A is a constant and /Theta is the angle through which the object has rotated. What is the final angular speed of the object?

    2. Relevant equations


    3. The attempt at a solution

    ##W=\Delta K\\ \int _{ 0 }^{ \frac { \pi }{ 2 } }{ \tau d\theta } =\frac { 1 }{ 2 } I\omega ^2\\ \\ \int _{ 0 }^{ \frac { \pi }{ 2 } }{ Acos\theta d\theta } =\frac { 1 }{ 2 } I\omega ^2\\ \\ \frac{A\pi}{2}=\frac { 1 }{ 2 } I\omega ^2\\\\\omega=\sqrt { \frac{A\pi }{I} }##


    Answer in the back of the book:


    ##omega=\sqrt { \frac{2A }{I} }##

     
  2. jcsd
  3. Jul 4, 2015 #2

    TSny

    User Avatar
    Homework Helper
    Gold Member

    Check your evaluation of the integral.
     
  4. Jul 5, 2015 #3
    yup, I see it now. I appreciate it. I am not sure how I missed that.

    Thanks again
     
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