# How to show that the total angular velocity vector of a rigid body is the sum of all angular velocity vectors acting on it

I am trying to prove the additivity propety for the angular velocity vectors acting on a body in three dimensions. Particularly also in the case when the axes of rotation do not cross each other (the body may not be rotating about a fixed point).

In plane motion it is easier to see. Grab two coins, fix one flat on a table and make the other one rotate around the edge of the fixed one without slipping. One can see that the total angle of rotation of the one rotating is 2 times the angle that it has traveled around the fixed one. One can build a proof from this for plane motion (the case when angular velocity vectors are parallel to each other) but i don't know how could one show the same thing for 3d.

• if you want a proof, find math majors. If you want to prove it to yourself it's just like planar except you have the additional z axis, so you the scalars turn into x,y,z. Apr 21 at 0:53