and there is nothing stopping us from looking at it that way with the skier in about an 8 m radius turn, considering his mass at his CoM and the axis about 7 m away from him) the skier is doing 4 times the rotational speed, but since the radius is only half as much, each rotation only takes him half as far across the snow, so he is really covering twice as much distance per second. Really the numbers were chosen to make the mass easier, in reality, he would be able to move his mass about 1/2 a meter, but it illustrates the effect, and at those distances and typical speeds his angular velocity and momentum are small. The angular momentum is quite small, compared to the linear momentum, except perhaps after a collisions that makes him spin. ; we will be arguing about gyroscopic effects next , and then Coriolis, but hey, let's account for every dyne and erg.
Its somewhat interesting to talk about angular velocity there, but angular momentum has a requirement that is not being met for all practical purposes.
My understanding about momentum is that momentum is a state of mass and velocity that if not acted upon by other forces, will continue in the same motion until something acts on it to change it.
Angular momentum is created or destroyed with torque. You spin a top and it spins without any other force until friction eventually stops it or you apply some reverse torque to slow it down. The angular velocity could change if you can change the moment of inertia, but momentum is preserved.
A skier traveling on a curved path does not posses any angular momentum as some are presenting. If nothing else acts on the skier, he will travel in a straight line, not a round circumference. There is not any angular momentum present. Continual external forces are causing it to travel on a curved path. A skier does not have angular momentum UNLESS he gets some torque introduced that will cause him to start spinning this way or that. Here are some examples of angular momentum in skiing:
- You hit a bump, your weight is too far forward. This causes a torque against the front of your feet which causes your body to rotate forward into a face slam
- You catch an edge going very fast which creates torque on your ski and cartwheel down the hill
- You crest a bump and your weight is too far back, gravity grabs your skis and pulls them down the hill, i.e., torque and your body spins backwards in angular momentum until you fall on your butt
- You take a jump and do various ariels in the air, with lots of angular momentum going on.
The turn shape does not qualify for angular momentum.