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Motion in a Rotating Reference Frame

1. The problem statement, all variables and given/known data

A particle moves in a rotating reference frame along the x-axis as x(t) = xo eat (xo and a are positive constants). The frame rotates with a time-dependant angular frequency ω(t) about the x-axis. The true physical force is in the x-direction of the rotating frame. Break up the equation relating the accelerations ar and af into x and y components.

2. Relevant equations

Equation relating frames' accelerations:
af = Af + ar + ω' x r + 2ω x vr + ω x (ω x r)

3. The attempt at a solution

I know that Af is zero because the frame's origin is not moving. I am just stuck when it comes to considering what is with respect to what. In my mind everything that is relative to the rotating frame (everything with an "r" subscript) has only an x component because motion is only happening in the x direction. And af is due to the true physical force which is also acting in the x direction. So r would be the only thing with a y component?

I am getting so mixed up with these inertial/non-inertial reference frames! What is going on here?
 
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