Rotational Motion

  • Thread starter rpthomps
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  • #1
182
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Homework Statement



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?

Homework Equations




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} }##

[/B]
 

Answers and Replies

  • #2
TSny
Homework Helper
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Check your evaluation of the integral.
 
  • #3
182
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yup, I see it now. I appreciate it. I am not sure how I missed that.

Thanks again
 

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