Angular velocity/speed

In this diagram what is omega?
Angular velocity or speed?
Why is the direction of angular velocity perpendicular to plane of rotation?

omega = 2.pi.f

where: 2.pi = 1 radian = 360^o

omega is therefore radians/sec.

Since speed = distance/time and is a scalar quantity (magnitide only), velocity is a vector quantity and therefore also has direction.

The arrow is therefore a direction component so omega for this queston is angular velocity.

Is there any difference between angular velocity or angular speed?
And why is the direction of angular velocity perpendicular to the plane of rotation like this: http://scripts.mit.edu/~srayyan/PERwiki/images/9/95/AngularKinematics02.png

thanks!

just amended original answer.

Is there any difference between angular velocity or angular speed?
And why is the direction of angular velocity perpendicular to the plane of rotation like this: http://scripts.mit.edu/~srayyan/PERwiki/images/9/95/AngularKinematics02.png

thanks!

I understand everything you have said, but i dont understand why the direction of angular velocity is perpendicular to the plane of rotation here:
http://scripts.mit.edu/~srayyan/PERwiki/images/9/95/AngularKinematics02.png

It's a poor depiction, but omega is a tangent to the axis of rotation. In this diagram it is not at all clear that is what is actually meant to be shown.

It's a poor depiction, but omega is a tangent to the axis of rotation. In this diagram it is not at all clear that is what is actually meant to be shown.

Its more clear in these pictures:
http://www.phys.ttu.edu/~batcam/Courses/semester%201/Labs/UNIT%2016%20ROTATIONAL%20DYNAMICS_files/image026.jpg
http://upload.wikimedia.org/wikipedia/commons/thumb/d/d5/Angular_velocity.svg/250px-Angular_velocity.svg.png

Is this true?

http://www.phyziczteacher.com/chap8v.bmp

Its more clear in these pictures:
http://www.phys.ttu.edu/~batcam/Courses/semester%201/Labs/UNIT%2016%20ROTATIONAL%20DYNAMICS_files/image026.jpg
http://upload.wikimedia.org/wikipedia/commons/thumb/d/d5/Angular_velocity.svg/250px-Angular_velocity.svg.png

Are you OK with my expalanation is post #10 ?

Yes, thank you!

This kind of definition is absolutely critical for referencing the correct direction of rotation wrt any given orthogonal axis system like that used for aircraft, missiles, gyroscopes, robotics etc.

Ahh i see, thank you!

On this image, is ar is the centripetal force and a(theta) is the linear acceleration, so the direction of acceleration would be the diagonal arrow?

Is this correct?

http://upload.wikimedia.org/wikipedia/commons/thumb/2/22/Nonuniform_circular_motion.svg/579px-Nonuniform_circular_motion.svg.png

There are two cases to consider:

a) Constant omega (constant angular velocity) where: equal angles are traversed in equal times. Because the velocity vector (tangent) is constantly changing direction and acceleration is defined as the rate of change of velocity, then constant circular motion is in fact a definition of acceleration.

That acceleration (a_r) is directed towards the axis center of rotation and since acceleration is a result of a force (Newtons laws), the force producing that acceleration must also be directed towards the axis of rotation. That force is defined as centripetal force and is always perpendicular to the tangential velocity vector.

b) Changing omega or non-uniform circular motion: where the angular speed is not constant. This is depicted in the diagram you posted. To produce that change in angular speed, there must be an additional tangential force acting to either slow or speed up the rotation. This is angular acceleration a_theta or d²theta/dt².

So the vector sum of the centripetal force producing (a_r) and the force producing the angular acceleration (a_theta) therefore is acting in the direction (a) shown in the diagram.