Direction of Angular Velocity (w)

[cosurfr]

Homework Statement

This problem is all conceptual and there is no calculations needed. My question is this:

A top is spinning counterclockwise as seen from above. It is also moving to the right with a linear speed v. What is the direction of the angular velocity vector w=theta/time

I know the answer is upward, I just don't understand why that is?

Does anyone have any explanations for me? Thanks in advance

Homework Equations

The Attempt at a Solution

 

[cosurfr]

Okay think i got it, but if someone would confirm that would be awesome.

Angular vel describes the speed of rotation. The direction of the velocity vector will be along the axis of rotation. Thus since the axis is pointing up, the angular velocity vector points up also.

Thanks again

cosurfr

 

[jgens]

Well, my best simple explanation is that the direction of the angular velocity follows the right hand rule (curl the fingers of your right hand in the direction of rotation and your thumb points in the direction of the angular velocity). A better explanation involves the angular velocity defined in terms of the vector cross product. The wikipedia page covers this a bit . . . http://en.wikipedia.org/wiki/Angular_velocity

Edit: Note that the angular velocity is really a psuedo-vector.

 

[cosurfr]

Okay I see. So the direction of the ang vel vector is always perpendicular to the plane of rotation. Visually i can see this now. Thanks for the link

cosurfr

 

[ideasrule]

By the definition of angular velocity, something spinning counterclockwise has its angular velocity vector pointing up. Why? Because if you rotate a screw or nut counterclockwise, it moves up. This is an arbitrary convention, of course; an alien might have screws threaded the other way and angular velocity vectors defined differently.