The torque is given by:
[tex]\tau=I\alpha[/tex]
where I is the moment of inertia of the disk and alpha is the angular acceleration.
The moment of inertia for a disk is given by:
[tex]I=\frac{1}{2}mr^2[/tex]
where m is the mass and r is the radius. The angular acceleration can be obtained from the relation:
[tex]\alpha=\frac{\omega^2_f-\omega^2_i}{2\theta}[/tex]
In this case the mass is 0.240 kg and the radius is 15.25 cm or 0.1525 meters. Furthermore, the initial angular velocity is zero, the final angular velocity is 3.49 rad/s and the angle it takes to reach it is 1.2 by 2pi. Plugging this in the equation for the torque we have:
[tex]\begin{gathered} \tau=(\frac{0.240\cdot0.1525^2}{2})(\frac{3.49^2-0^2}{2(1.2\cdot2\pi)}) \\ \tau=2.0663\times10^{-3} \end{gathered}[/tex]
Therefore the torque the motor must deliver is:
[tex]2.0663\times10^{-3}\text{ Nm}[/tex]
