Confused about uniform circular motion (and it's velocity vector)

[Tobias101]

Sorry if this is the wrong (sub)forum!

I need some help to understand how to express the following:

The velocity vector


When this is given:

Omega
radius

Both in magnitudes. I want to obtain an expression for the velocity vector when the angle theta (radians/s) is changed. That is, when i know the position of the particle:

(x,y) = r*(cos(theta),sin(theta)) Note: center is at (0,0)

I know the velocity vector is tangent to the point on the circle at any given time, and that it can be determined via the cross-product between the vectors omega and r, that is:

V = Omega X r

But how do i convert from magnitudes to vector form?? - it's very simple, I'm sure of it, but i cannot see anything in my book in calculus...

Any help appreciated - i hope i made myself clear

 

[jbsteele]

! The velocity vector can be expressed as: V = (Omega * radius * sin(theta), -Omega * radius * cos(theta)). This is derived by taking the cross product of Omega and r, where Omega is expressed as a unit vector in the z direction (0, 0, 1) and r is expressed as (radius * cos(theta), radius * sin(theta), 0). The resulting velocity vector will have components in the x and y directions.