# 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

• 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