Velocity example, a car moving at a constant 20 kilometres per hour in a circular path has a constant speed, but does not have a constant velocity because its direction changes. Hence, the car is considered to be undergoing an acceleration. Speed describes only how fast an object is moving, whereas velocity gives both how fast it is and in which direction the object is moving. If a car is said to travel at 60 km/h, its speed has been specified. However, if the car is said to move at 60 km/h to the north, its velocity has now been specified.
Angular velocity a true vector, rather than just a pseudo-vector. The only non-obvious property of the above addition is commutativity. This can be proven from the fact that the velocity tensor "W" (see below) is skew-symmetric, so that formula_34 is a rotation matrix which can be expanded as formula_35. The composition of rotations is not commutative, but formula_36 is commutative to first order, and therefore formula_37. Notice that this also defines the substraction as the addition of a negative vector. Given a rotating frame of three unit coordinate vectors, all the three must have the same angular speed at each instant. In