Pendulum attached to a rotating vertical disk

[ChiralSuperfields]

Homework Statement

I try to derive coordinates for a mass on a rotating pendulum using a different coordinate system

Relevant Equations

$$(x,y)$$

For this problem,

I correctly got the same coordinates for the pendulum mass using another coordinate system. The coordinate system I used was the other coordinate system rotated counterclockwise by 90 degrees. Why is the pendulum mass coordinates invariant in my cartesian coordinate system (x̄,ȳ)?

Thanks for any help!

 

[haruspex]

Homework Statement: I try to derive coordinates for a mass on a rotating pendulum using a different coordinate system
Relevant Equations: $$(x,y)$$

For this problem,
View attachment 343207
I correctly got the same coordinates for the pendulum mass using another coordinate system. The coordinate system I used was the other coordinate system rotated counterclockwise by 90 degrees. Why is the pendulum mass coordinates invariant in my cartesian coordinate system (x̄,ȳ)?

Thanks for any help!

Do you mean that your system was x positive to the right and y positive up?
In that system it would be ##x=a\cos(\omega t)+b\sin(\theta)##, ##y=a\sin(\omega t)-b\cos(\theta)##.

 

[ChiralSuperfields]

Do you mean that your system was x positive to the right and y positive up?
In that system it would be ##x=a\cos(\omega t)+b\sin(\theta)##, ##y=a\sin(\omega t)-b\cos(\theta)##.

Thank you for your reply @haruspex!

Yes you are correct!

Thanks!