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

[sulemanma2]

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?

 

[Pythagorean]

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.

 

[AJ Bentley]

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)

 

[sulemanma2]

So there is no mathematics involved in why it is perpendicular, it is just defined that way to help us visualize it?

 

[rcgldr]

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.

 

[AJ Bentley]

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!

 

[zeromodz]

Its perpendicular to the radius because its angular. It is going the other way.