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DISCUSSION and HINTS
As can be seen from the animation below, the path taken by P is a bit complex. However, what if we put an observer on the non-extending section of the rotating arm - what motion would the observer see for P? Think about that.
Suppose that we do put an observer on the non-extending portion of the rotating arm. That observer would describe the motion of P as being on a straight path aligned with the x-axis. Specifically, we have:
(vP/O)rel = L_dot i
(aP/O)rel = L_ddot i
Using this observer, we can write down the velocity and acceleration of P using the moving reference frame velocity and acceleration equations:
vP = vO + (vP/O)rel + ω x rP/O
aP = aO + (aP/O)rel + α x rP/O + 2ω x (vP/O)rel + ω x (ω x rP/O)
where ω and α are the angular velocity and angular acceleration, respectively, of the observer.