What is the velocity of a point inside an infinite rotating rod?

[TheFlatlander]

Hi guys, I'm new here so thanks for any guidance...
Using vector notation, I need to find the velocity of an infinite rod, rotating with frequency, ω, centred on the z axis. (rotating about z-axis in the anti-clockwise direction when viewed from above).

I need to give the velocity in terms of a charge the point r = (x, y, z) which is inside the rod
(eg r┴ = (√x²+y²) < radius of the rod, a )
The charge itself is not important, I simply need to find the velocity V of it.

I have a vague idea as to how to do this:
I know that the velocity is perpendicular to both r and the z-axis, so it probably involves some sort of cross product?
Using the unit vector k multiplied by r/|r| ?

I am pretty clueless with this one guys, despite it only being simple vector manipulation... Any help would be greatly appreciated!
Thanks in advance

 

[chaoseverlasting]

You've got it right, its cross product manipulation. Do you know of any relation between angular velocity and translational velocity?

 

[tiny-tim]

Draw a diagram!

Hi TheFlatlander! Welcome to PF!

It often helps to draw a diagram (a rough one).

Draw a diagram with the x and y axes, and a typical point r.

Now draw in where r goes during the rotation (I don't mean instantaneously, I mean for the next hour or so).

You know the frequency (w). Does that tell you how far it goes in any particular time?

If so, you have the speed (not the velocity, of course). So what is the velocity? Draw it on the diagram, then write it as a vector.

 

[TheFlatlander]

Thanks for the tips guys. I got there in the end.