A pulley of radius $1.5 \mathrm{~m}$ is rotated about its axis by a force $F=\left(12 \mathrm{t}-3 \mathrm{t}^{2}\right) N$ 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 ___________.