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

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SUMMARY

The discussion centers on the relationship between angular velocity (ω) and its perpendicularity to the plane of rotation, defined by the equation V = ωr. It establishes that ω is perpendicular to the plane of rotation due to its alignment with the axis of rotation. The formula ω = (r x v)/|r|² is confirmed as a representation of the cross product, which mathematically demonstrates this perpendicularity. The use of the cross product in the equation ω = vsinθ χ 1/r further clarifies the geometric interpretation of angular velocity.

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  • Understanding of vector mathematics and cross products
  • Familiarity with angular motion concepts
  • Knowledge of the relationship between linear velocity and angular velocity
  • Basic principles of rotational dynamics
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  • Explore the derivation of angular velocity equations in rotational dynamics
  • Learn about the implications of angular momentum in physics
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Physics students, mechanical engineers, and anyone interested in the mathematical foundations of rotational motion and dynamics.

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?
 
Physics news on Phys.org
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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