# 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?

• One thing you could do is break both F_x and F_y in Fig 1 into parts tangential and normal to the curve (i.e., the directions used in Fig 2). Then you would see that the tangential parts of F_y and F_x combined equal the F_y of the second diagram (and the normal parts sum to F_x). It's not that I can see this at a glance, but mathematically it must be true.
– A_P
Sep 24, 2022 at 14:58

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.
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.