Answer
The motor must deliver a torque of $1.24\times 10^{-3}~N \cdot m$
Work Step by Step
We can find the angular acceleration:
$\omega_f^2 = \omega_0^2+2\alpha~\Delta \theta$
$\alpha = \frac{\omega_f^2 - \omega_0^2}{2~\Delta \theta}$
$\alpha = \frac{(3.49~rad/s)^2 - 0}{(2)(4\pi~rad)}$
$\alpha = 0.485~rad/s^2$
We can find the required torque:
$\tau = I~\alpha$
$\tau = \frac{1}{2}MR^2~\alpha$
$\tau = \frac{1}{2}(0.22~kg)(0.1525~m)^2~(0.485~rad/s^2)$
$\tau = 1.24\times 10^{-3}~N \cdot m$
The motor must deliver a torque of $1.24\times 10^{-3}~N \cdot m$
