Answer
$\alpha =17 rad/s^2$
Work Step by Step
To find the acceleration, use a kinematics formula relating angular acceleration, initial angular velocity, final angular velocity, and angular displacement. This is $$\omega_f^2=\omega_o^2+2\alpha \Delta \theta$$ Solving for angular acceleration $\alpha$ yields $$\alpha=\frac{\omega_f^2-\omega_o^2}{2\Delta \theta}$$ 2.5 revolutions must be converted to rad/s using dimensional analysis. $$2.5 rev \times \frac{2\pi rad}{1rev}=5\pi rad$$ Substituting known values of $\Delta \theta=5\pi rad.$, $\omega_o=12rad/s$ and $\omega_f=26 rad/s$ yields an angular acceleration of $$\alpha=\frac{(26rad/s)^2-(12rad/s)^2}{2(5\pi rad.)}=17rad/s^2$$
