The torque $\tau$ is related to the moment of inertia $I$ and angular acceleration $\alpha$ by Newton's second law for rotation: $\tau = I\alpha$. The angular acceleration is assumed to be constant. The final angular velocity is $\omega = 2\pi f$. Using the rotational kinematic equation $\omega = \omega_0 + \alpha t$, with initial angular velocity $\omega_0 = 0$:

$$\alpha = \frac{\omega}{t} = \frac{2\pi f}{t}$$

Substituting this into the torque equation:

$$\tau = I \frac{2\pi f}{t}$$ $$\tau = (50 \text{ kg} \cdot \text{m}^2) \frac{2\pi (2 \text{ r/s})}{0.5 \text{ s}} = 400\pi \text{ N}\cdot\text{m}$$