Regarding the direction of the angular velocity vector

sharpstones

If a top is spinning in the horizontal x,y planes in a counter-clockwise motion, the vector of its angular velocity and acceleration is perpendicular to that plane, specifically in the positive z direction.
Is there any specific reason for direction? My book states that the vector must be perpendicular to the plane of motion so that is unique regardless of whether you observe the object from its top or bottom, but this answer does not seem very satisfactory. Is there another reason? Or is it really arbitrarily based on the fact that when our thumbs curl in a counter-clockwise motion our thumb points upward?

himanshu121

it is a vector product, And the direction is related with axis of rotation

sharpstones

I really do not understand what you mean. I do understand that yes it is a vector product, but i don't understand what you mean by how it is related to the axis of rotation, unless you are referring to what I have already said about how the direction is related to the axis of rotation through the "right hand rule"

Tron3k

It is based on the cross product, which is based on the right-hand-rule, which is of course totally arbitrary. It is only important that we be consistent.

You can check it out at ScienceWorld.

himanshu121

i meant to say that the vector is || axis of rotation

selfAdjoint

Suppose you yourself were going to create a vector to represent angular momentum of something spinning in the x-y plane. There's no problem about the magnitude (length), it's the amount of angular momentum - fine!

But what direction can you point it? Any direction in the x-y plane would be as good - or as bad - as any other, because any point on a spinning object points in all the directions in the plane of rotation as it goes around. So selecting any one direction in the plane and saying "that's it" is a bonehead play.

All that's left are the two directions normal to the the plane - up and down. Now it's an even call which one you pick, and long ago they picked according to the "right hand rule" which you may have heard of. Curl the fingers of your right hand in the direction of the spin and stick out your thumb. The direction your thumb pooints is the direction of the A.M. vector.

Njorl

A bit OT, but it is about right hand rule.

A proctor, before a large basic physics exam on magnetism told us this. With 500 people taking the exam, there are always a few holding up their right hand and curling their fingers. And every once in a while, there's some guy holding up his left hand and doing it.

Njorl