ANGULAR MOMENTUM
 we defined the angular momentum  of a mass m traveling at a speed v in a circle of radius r as
= mvr .......(1)

Figure 1 :Ball on the end of a string, swinging in a circle.

As we saw, in Figure (1) reproduced here, the quantity = mvr did not change when we had a ball moving in a circle on the end of a string, and we pulled in on the string. The radius of the circle decreased, but the speed increased to keep the product vr constant.
This was our introduction to the concept of the conservation of angular momentum.
After that, we went on to consider some rather interesting experiments where we held a rotating bicycle wheel while standing on a freely turning platform. We found that these experiments could be explained qualitatively if we thought of the angular momentum of the bicycle wheel as being a vector quantity  which pointed along the axis of the wheel, as shown in Figure (2) reproduced below. What we will do now is develop the formalism which treats angular momentum as a vector.

Figure 2: When the bicycle wheel is turned over and its angular momentum points down, the person starts rotating with twice as much angular momentum, pointing up.