A pulley of radius 1.5 m is rotated about its axis by a force F=(12 t -3 t^2) N applied tangentially (while t is measured in seconds). If moment of…

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