How to draw vectors? The images show rotational motion.Here, $r$ is the position of the particle and $F$ is the force applied on it.
Now, if I draw vectors $F_x$ and $F_y$ according to fig.2, I understand why it moves in a circular path.My confusion is in fig.1. My teacher derived the expression of torque using fig.1. What I can't understand is how $F_y$ can can help move the particle in circular path?

 A: For one thing, if $F_x$ and $F_y$ are components of $\vec F$, they are usually drawn not to extend beyond the projection of $\vec F$ in that direction. E.g. the $F_x$ arrow in Fig 1 should be much shorter, and $F_y$ in Fig 2 should be much shorter.
You can choose any set of orthogonal directions and call it "$x$ and $y$," so in that sense either figure is correct, but I will say Fig 2 seems like a more natural choice for the problem, tangential and radial to the circle.
A: For the purpose of calculating torque, both the figures provide good choices. If you know coordinate of the the point where force $\vec{F}$ acts, taking components of $\vec{F}$ along directions parallel to coordinate axes, as in Fig. 1, may help. If you know the radius of the circle, taking the components as in Fig. 2 may be better.
However, it may be easier to visualize the intended circular path, at least for beginners, if the force is resolved as in Fig. 2 because then they can see the components as tangential and radial components. But, even if you are presented with Fig. 1, you can mentally resolve the component $F_y$ along tangential and radial directions. Here, I am saying to (mentally) resolve a component ($F_y$) along two perpendicular directions just to understand that there are indeed tangential and radial components of force $\vec{F}$ just like as in Fig. 2. But actually resolving a component again into components is often not useful and can lead to confusion and hence must be avoided.
