A pulley of radius 1.5 m is rotated about its axis by a force $\mathrm{F}=\left(12 \mathrm{t}-3 \mathrm{t}^2\right) \mathrm{N}$ applied tangentially (while t is measured in seconds). If moment of inertia of the pulley about its axis of rotation is $4.5 \mathrm{~kg} \mathrm{~m}^2$, the number of rotations made by the pulley before its direction of motion is reversed, will be $\frac{K}{\pi}$. The value of $K$ is $\_\_\_\_$ .