Movement of a point on the perimeter of a disc

[charbon]

Homework Statement

a disc of radius r spins uniformly around its axis at an angular velocity $$\omega$$ in a clockwise motion. the center moves on the horizontal line z = r of a vertical axis Oxz of the referential Oxyz. We call R' = Cxyz, in translation compared to R= Oxyz, of origin C and we specify $$\theta$$ the angle made by a CA from the disc with Cz, A being a point of the perimeter of the disc.

a) express in R, the velocity and acceleration of A compared to R'
b) What velocity, in R, must we give to C in order for the velocity $$\vec{vb}$$/R of the lowest point of the disc be 0?

Homework Equations

I am having a hard time finding b)

first off, I wrote the velocity-addition formula

$$\vec{vb}$$ = $$\vec{vb'}$$ + $$\vec{V}$$
thus
$$\vec{V}$$ = $$\vec{vb}$$ - $$\vec{vb'}$$

but $$\vec{vb}$$ = 0
so
$$\vec{V}$$ = - $$\vec{vb'}$$

This is where I am stuck. How do I find this vector?

 

[BigJDubs]

The Attempt at a SolutionI tried using the definition of velocity of a point A in an inertial frame, v_A = \frac{d\vec{r}}{dt}where \vec{r} is the position vector of A relative to Oso I wrote\vec{vb'} = \frac{d\vec{r}}{dt}where \vec{r} = rcos\theta \hat{i} + rsin\theta \hat{j}but I am not sure if this is the correct approach and if so how do I continue?