Angular velocity vector in terms of motion of an object May be it is small question in this forum but I'm trying to get the feel of the understanding about the angular velocity. If this question is getting rejected please kindly refer me to appropriate forum.
From the definition of angular velocity the directory vector of angular veloticy is perpendicular to the plane of the rotation. It seems to make sense for electro-magnetic phenomenon, wherein direction of magnetic field when current is passing though a solenoid or something of torque, where in the direction of the screw can be sensed as angular velocity. But in mechanical terms i.e rotation of an object around a fixed radius, what does it mean some component acting perpendicular to the plane of rotation of the object. Nothing is moving, then why such a concept so developed. I mean what problem it is going to solve and so invented and devised. Please explain.
 A: Angular velocity of aan object is defined as the change of angle per unit time, $\omega =\frac{\delta \phi} {\delta t} $. So you end up with a circular motion around an origin,  and as a result the object moves in a plane defined by the radius r and the angle $\phi$. The direction of the angular velocity vector is chosen normal to this plane. Now there are two directions the movement can take, either clockwise or counterclockwise. Following the mathematical definition of the normal vector the direction of the angular velocity vector is chosen towards you if you observe the motion to be counterclockwise, and away from you if you observe the motion to be clockwise. 
The same definition applies to direction of magnetic field in a solenoid, the Lorentz force and to the definition of torque. But you make an error when you think that the direction of torque or angular velocity states something about a motion in that direction. Most of our screws are right turned, resulting in the observed behavior. But left turned screws do exist and the move against the direction of torque. 
