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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} }##
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