$...$PROBLEM $1$

A pin $($point $P)$ slides along a slot on a rotating arm and a slot on fixed horizontal plate.

$($a$)$ How many degrees of freedom does the system have?

$($b$)$ Draw one rotating reference frame and the angle that describe the orientation of these frames with respect to frame $A$ on the figure above.

$($c$)$ Write the position of point $P$ with respect to the frame $A(r^{OP})$ using unit vectors of rotating frame $($only use unit vectors of frame A when necessary$).$

$($d$)$ Write the position of point $P$ with respect to the frame $A(r^{0P})$ using only the unit vectors of frame A$.$