12.8 rad
Explanation:
The angular displacement [tex]\theta[/tex] through which the wheel turned can be determined from the equation below:
[tex]\omega^2 = \omega_0^2 + 2\alpha\theta[/tex] (1)
where
[tex]\omega_0 = 0[/tex]
[tex]\omega = 34.7\:\text{rad/s}[/tex]
[tex]\alpha = 47.0\:\text{rad/s}^2[/tex]
Using these values, we can solve for [tex]\theta[/tex] from Eqn(1) as follows:
[tex]2\alpha\theta = \omega^2 - \omega_0^2[/tex]
or
[tex]\theta = \dfrac{\omega^2 - \omega_0^2}{2\alpha}[/tex]
[tex]\:\:\:\:= \dfrac{(34.7\:\text{rad/s})^2 - 0}{2(47.0\:\text{rad/s}^2)}[/tex]
[tex]\:\:\:\:= 12.8\:\text{rad}[/tex]
