Answer
$F = 3.05~N$
Work Step by Step
We can find the angular acceleration:
$\alpha = \frac{\omega}{t}$
$\alpha = \frac{317~rad/s}{15.5~s}$
$\alpha = 20.45~rad/s^2$
We can find the required torque:
$\tau = I~\alpha$
$\tau = \frac{2}{5}MR^2~\alpha$
$\tau = (\frac{2}{5})(1.65~kg)(0.226~m)^2~(20.45~rad/s^2)$
$\tau = 0.689~N~m$
We can find the required force:
$R~F = \tau$
$F = \frac{\tau}{R}$
$F = \frac{0.689~N~m}{0.226~m}$
$F = 3.05~N$
