[Physics] What actually is the vector of angular momentum

angular momentumangular velocitymoment of inertiarotational-kinematicsvectors

If an object spins around a central point, it gets angular momentum which is a vector with an orientation dependent on whether its clockwise rotation or anticlockwise, i get that. But what the vector part actually is, is confusing me. Does it mean that the object spinning gets a force going upwards or downwards? In that case, how do you explain bicycles? Shouldn't the spinning result in angular momentum pointing in one direction thus forcing your bike to fall over the same way someone would if they pushed you from either side of the bike?

Best Answer

Angular momentum has a magnitude, and is about some axis (thus has some sense of "direction). So vectors are used to represent the quantity, and much of the machinery of vectors applies to it. However, there are ways in which "vector" is a misleading term when applied to it, and some people characterize them as being in other mathematical structures, such as a Clifford algebra. Regardless of the exact mathematical formulation, they do not live in the same "space" as the physical world. The vector that represents angular momentum has physical meaning, but it doesn't physically exist. If an angular momentum is represented by a vector pointing east, that doesn't mean that there is any physical thing pointing east. It just means that the angular momentum is around an east-west axis, and that it is "positive" in the eastern direction, where "positive" is an arbitrary convention that we use to keep track of direction.

And apart from all the above, angular momentum is not a force, any more than linear momentum is. It is rotation around an axis.