Understanding Angular Velocity: Why is it Perpendicular to Circular Motion?

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Discussion Overview

The discussion centers on the nature of angular velocity and its relationship to circular motion, specifically why angular velocity is considered to be perpendicular to the direction of motion in a circular path. Participants explore theoretical and conceptual aspects of this relationship.

Discussion Character

  • Conceptual clarification
  • Debate/contested
  • Technical explanation

Main Points Raised

  • One participant questions whether angular velocity should be parallel to circular motion since it measures the change in angle over time.
  • Another suggests that the perpendicular nature of angular velocity is a convention, noting that a spinning disk in the XY plane cannot be described by a single direction.
  • A different viewpoint emphasizes that describing a plane by the direction of its normal is convenient, and that rotation in a plane often leads to forces along the normal direction.
  • Some participants argue that the perpendicularity is merely a definition for visualization purposes, with no mathematical necessity behind it.
  • It is mentioned that performing math on vectors related to angular velocity is easier than developing rules for planes or discs.
  • One participant points out the limitations of this convention, noting that rotations are not commutative, which complicates the addition of rotation vectors.
  • Another participant asserts that angular velocity is perpendicular to the radius because it is angular in nature, implying a directional aspect to the motion.

Areas of Agreement / Disagreement

Participants express a mix of views regarding the nature of angular velocity and its perpendicularity to circular motion. While some see it as a convention, others highlight its practical implications and the challenges in mathematical representation. No consensus is reached on whether the perpendicularity is fundamentally justified or merely a definitional convenience.

Contextual Notes

Participants acknowledge the lack of a mathematical basis for the perpendicularity of angular velocity, indicating that this discussion may depend on definitions and conventions rather than established mathematical principles.

sulemanma2
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Can anyone explain why angular velocity is perpendicular (or goes up and down) to the circular motion

I know that angular velocity measures the change angle over time, so wouldn't that mean the angular velocity is parallel to the circular motion since the angles are measured parallel to the circle? Or am I confusing myself?

someone on yahoo asked this question but the answers to it didn't make sense to me:

http://in.answers.yahoo.com/question/index?qid=20100113090226AAXyK1A

In one of the answers it says that the angle is measured by taking a route along the Z direction? why is that?
 
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I think it's just a convention. If a disk were to spin in the XY plane, you couldn't say it's going in -x or +x or -y or +y direction, because it's doing all of that at different parts on the disc.

On the other hand, in QM, angular momentum is a consequence of the third dimension. Not sure what bearing that has on a classical scheme, so I desist.
 
It's basically a convention but with an eye on a couple of facts that justify it.

a) It's convenient to describe a plane by the direction of it's normal (perpendicular to the surface) and rotation takes place in two dimensions i.e. in a plane.

b) There are lots of circumstances in nature where rotation in a plane leads to a force or a movement along the normal. (a screw thread is a simple mechanical example - there are also several in electromagnetic experiments)
 
So there is no mathematics involved in why it is perpendicular, it is just defined that way to help us visualize it?
 
It's easier to perform math on vectors, in this case the axis of rotation, than to invent a set of rules to perform math on planes or discs that represent angular velocity, acceleration, or force.
 
sulemanma2 said:
So there is no mathematics involved in why it is perpendicular, it is just defined that way to help us visualize it?
That's right.

It's not even a particularly useful convention for a lot of purposes.
For example, it would be really nice if you could add two rotation vectors to get a resultant rotation. But you can't - rotation is not commutative, the order in which you perform the rotations affects the outcome, whereas adding two vectors regardless of order gives the same result. Pity, but there you are!
 
Its perpendicular to the radius because its angular. It is going the other way.
 

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