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

AI Thread Summary
The discussion centers on the relationship between angular velocity (ω) and the cross product in determining perpendicularity to the plane of rotation. The formula V = ωr illustrates how velocity (V) relates to angular velocity and radius (r). It is suggested that the direction of ω is perpendicular to the plane of rotation because it aligns with the axis of rotation. The cross product of vsinθ and 1/r is proposed as a mathematical explanation for this perpendicularity. Overall, the discussion emphasizes the geometric and mathematical principles that define the orientation of angular velocity in rotational motion.
Miraj Kayastha
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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?
 
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ω is perpendicular to the plane of rotation because it is parallel with the axis of rotation.
 
ω = (r x v)/|r|2
 

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