Why does the angular velocity vector point perpendicular to the plane of rotation?

Is this just convention or is there are physical meaning to the way the angular velocity vector points?|||It does NOT have physical meaning in the sense of something physical actually "pointing" in that direction. But it is a very useful mathematical convention. In particular, it allows you to use standard vector math to relate angular velocity, angular momentum, angular accelation and torque. It allows you to adopt a useful definition of angular momentum in terms of the cross-product of two vectors (the linear velocity vector of a particle on the rotating object, crossed with its displacement vector from the axis), and similarly define torque as the cross product of two vectors (force × displacement from axis).





If you adopt all these conventions for the various vectors, you can then write vector relationships for torque, angular momentum, angular acceleration and angular velocity, which are exact analogs of the vector relationships for force, linear momentum, linear acceleration and linear velocity.|||It has physical meaning. Look at how a Gyro-compass works. It takes force to change the direction of the angular velocity and angular momentum vectors. In aircraft, the gyro-compass it adjusted to point to True North (usually) at engine start-up. The aircraft can then turn in any direction and the vectors will keep the gyroscope pointed north





http://en.wikipedia.org/wiki/Gyro_compas…


http://en.wikipedia.org/wiki/Angular_mom…


http://en.wikipedia.org/wiki/Angular_vel…