[UPSC CSE 2022] Rotating Frame (Q142, 15M)

Consider two frames of reference $S$ and $S$ having a common origin $O$ . The frame $S$ is rotating with respect to the fixed frame $S$ with a uniform $\vec{\omega}=3a_x\,\mathrm{rad\,s^{-1}}$ . A projectile of unit mass at position vector $\vec{r}=7a_x+4a_y\,\mathrm{m}$ is moving with $\vec{v}=14a_y\,\mathrm{m\,s^{-1}}$ . Calculate in the rotating frame $S$ the following forces on the projectile:

(i) Eulers force

(ii) Coriolis force