**Rolling without slipping**

The observed motion of a point depends on the motion of the observer. Consider point P on the robotic arm shown below. Three GIFs are shown below the provide the view of the motion of point P as seen by three observers: i) an observer on fixed ground; ii) an observer attached to link OA; and, iii) an observer attached to link AP.

* Observer on link OA*Here, the observed path of P is complicated. The observed motion includes the rotation of both links OA and AP.

* Observer on link OA*Here, the observer is aware of only the rotation of AP about point A. Therefore, the observed path of P is a circle centered on A.

* Observer on link AP*With the observer on the same rigid body at P, the observer is unaware that point P actually moves. Therefore, the observer sees a stationary point P. The observer also sees link OA rotating in the clockwise sense, when, in fact, it is rotating in the counter-clockwise sense.

* Question*: Which observer do you think would be most useful in calculating the velocity and acceleration of point P?