# Rotational Motion

1. Jul 4, 2015

### rpthomps

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. Jul 4, 2015

### TSny

Check your evaluation of the integral.

3. Jul 5, 2015

### rpthomps

yup, I see it now. I appreciate it. I am not sure how I missed that.

Thanks again