Q$3$: Bar OA has a counterclockwise angular velocity ${}_0=2ra\frac{d}{s}.$ Rod BC slides freely through the pivoted collar attached to OA$.$

$(1)$ On the diagram below, write the coordinate frames vou will use for the equations:

$(2)$ Write the expression for the velocity of A with respect to O $.$ Simplify.

$(3)$ Write the expression of the velocity of A with respect to rod $BC.$ Simplify.

$(4)$ Determine the value of the angular velocity ${}_{BC}$ of rod $BC$ and the relative veloci to rod BC$.$

$$

$$

$(5)$ BONUS: What are the values of angular accelerations ${}_{OA}$ and ${}_{BC},$ as well as of the collar with respect to rodBC$(a_{\frac{A}{B}C}).$