Deriving Velocity Field of Rotating Plate Using v = ω × r

[crystalplane]

Homework Statement

A thin, circular plate assumed to lie on the xy-plane is rotating about its center, located
at (0, 0), with angular speed ω. (ω > 0 means that the plate is rotating in the counterclockwise direction.) Show that the velocity field of of this plate is given by v(x, y) = −ωyi + ωxj.
You must derive this result from an examination of the trajectories of points on the plate, and not

Homework Equations

v = ω × r

The Attempt at a Solution

based on the formula v = ω × r,” where ω = ωk is the angular velocity vector
But, the prof said that i can't simplely write v = ω × r..
** hope someone would like to help me get the correct answer**

 

[Topher925]

You are using rectangular coordinates, not tangential-normal coordinates. I believe you need to better describe the "r" term.