Given: Initial angular velocity, $\omega_0 = 0$ Moment of inertia, $I = 1.2 \text{ kg m}^2$ Rotational kinetic energy, $K = 1500 \text{ J}$ Angular acceleration, $\alpha = 25 \text{ rad/s}^2$

The rotational kinetic energy is given by: $K = \frac{1}{2} I \omega^2$ $1500 = \frac{1}{2} \times 1.2 \times \omega^2$ $1500 = 0.6 \omega^2$ $\omega^2 = \frac{1500}{0.6} = 2500$ $\omega = 50 \text{ rad/s}$

Using the kinematic equation for rotational motion: $\omega = \omega_0 + \alpha t$ $50 = 0 + 25 \times t$ $t = \frac{50}{25} = 2 \text{ s}$