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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?

enter image description here

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  • $\begingroup$ 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. $\endgroup$
    – A_P
    Sep 24, 2022 at 14:58

2 Answers 2

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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.

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  • $\begingroup$ Sorry for the bad figures. I still dont understand how fig 1 make sense. But thnx for answering. $\endgroup$
    – Rx6rx
    Sep 24, 2022 at 13:40
  • $\begingroup$ Indeed, I've redrawn that picture a bit for net force being complied to vector addition rules. $\endgroup$ Sep 24, 2022 at 14:11
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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.

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    $\begingroup$ Thnx for answering $\endgroup$
    – Rx6rx
    Sep 25, 2022 at 2:53

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