Taking Energy from a Flywheel

A rotating disk flywheel stores energy in kinetic form. Suppose a load converts the flywheel kinetic energy into electrical energy at a constant rate (in Watts).

When the load is first applied, the flywheel angular speed and its derivative are $(\omega_0, \dot{\omega}_0)$ . At some later time, the angular speed and its derivative are $( \frac{1}{2} \omega_0, \beta \, \dot{\omega}_0)$ .

What is the value of $\beta$ ?