Answer
$\tau = 1.12\times 10^4~N\cdot m$
Work Step by Step
We can find the angular speed:
$\omega = (320~rev/min)(\frac{2\pi~rad}{1~rev})(\frac{1~min}{60~s}) = 33.51~rad/s$
We can find the angular acceleration:
$\alpha = \frac{33.51~rad/s}{6.70~s}$
$\alpha = 5.00~rad/s^2$
We can find the required torque:
$\tau = I~\alpha$
$\tau = \frac{1}{3}ML^2~\alpha$
$\tau = (\frac{1}{3})(110~kg)(7.80~m)^2~(5.00~rad/s^2)$
$\tau = 1.12\times 10^4~N\cdot m$
