# Does changing the angle of a pendulum also shift the coordinate plane w.r.t which we give rectangular components to the $mg$ vector?

So given a simple pendulum, which makes an angle of 0 with the vertical axis in it's resting position.Now the pendulum is moved to a side by an angle $$\theta$$ with the vertical axis. The components of the vector $$mg$$ acting on the pendulum are given as: $$F_x = mg \sin \theta$$ $$F_y = mg \cos\theta$$ My question is that given the way the components seem to shift by an angle $$\theta$$ when the pendulum was shifted, like before moving the pendulum to the side the component would have been exactly parallel to x and y axis respectively but after moving the pendulum the component also change by an angle which may or may not be $$\theta$$, is the entire coordinate system shifting by this angle $$\theta$$ or some other angle for the vector $$mg$$?

Or just let me know what I'm doing wrong here? Or like my understanding about which part is flawed? Would really appreciate any help.

• Am I explaining this really badly? Sep 26 '19 at 19:17

## 1 Answer

No, the coordinate plane is fixed and the rectangular components assigned are with respect to this fixed coordinate axis. What is really happening is that in order to simplify the problem, we split the vector into components so that we can find stuff like the tension in the wire.

• No but the components seem to literally change their direction as the pendulum is moving by an angle. The only thing the components seem "fixed" to is the pendulum itself. The vertical component remains parallel to the pendulum and the horizontal remains perpendicular to it? What's up with that, this is exactly the problem I have, the plane SHOULD remain fixed but it is fixed w.r.t the pendulum itself instead of the actual x and y axis. And hence when the pendulum swings by some angle the components rotate by that angle also. Sep 26 '19 at 19:28
• The components seem fixed to the pendulum because the we have defined it in such a way. Else they wouldn't be very useful would they?
– Sam
Sep 26 '19 at 19:34
• Yep makes sense, cause otherwise the $mg$ vector is always with maximum vertical component and zero horizontal. It's just that conventionally it's been hammered into my head that coordinate system must always be fixed at x and y axis Sep 26 '19 at 19:39
• You could just as easily argue that the coordinate system is rotating though. Sep 26 '19 at 19:57
• @AaronStevens Welp that's exactly what it seemed like to me Sep 26 '19 at 20:03