Then I multiplied the acceleration by the moment of inertia to come up with:

[tex]\tau=.0197\text{Nm}[/tex]

...however the above is incorrect. Could someone please tell me why? I have gone through my steps many times, meaning that the only way this could be wrong is if I took the wrong steps; my arithmetic is fine. I'd appreciate any input on this.

your procedure is correct ... your final solution for tau does have some round-off error in it from rounding the final omega from the 1st part of the problem ... 9.4 rad/s.

If you don't round, you should get tau = .0913092394 Nm

If this is an on-line problem that is machine graded, that could be the reason.