How Does the Cross Product Determine the Perpendicularity of Angular Velocity?

[Miraj Kayastha]

V = ωr

V= velocity
ω = angular velocity
r = radius

How is the direction of ω perpendicular to the plane of rotation?

Is the formula ω = vsinθ χ 1/r which is the cross product of vsinθ and 1/r the reason why ω is perpendicular to the plane of rotation?

 

[paisiello2]

ω is perpendicular to the plane of rotation because it is parallel with the axis of rotation.

 

[dauto]

ω = (r x v)/|r|²