Ghost, appreciate all the details, but a few questions for you:

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Originally Posted by

**Ghost**

You can move your CoM by raising it with a push, in which case you have increased you potential energy, and that energy can later be converted into kinetic energy (and therefor more speed) when you come back down. You can also convert speed into potential energy by skiing up hill.

Isn't the pushing, in and of itself creating kinetic energy in the form of acceleration in a new direction? By pushing, you create force, ie, acceleration, which creates motion, which is kinetic energy.

The fact that gravity is there waiting just means that the higher you get away from some height, the potential to fall is great. By that logic, at the top of a ski run we have an incredible amount of potential energy ready to be turned into kinetic energy, ie motion. Which is true, but somewhat irrelevant for a discussion about ski turns.

To a certain degree the discussion of kinetic and potential energy is a bit academic for discussion about ski turns, where manipulation of forces is what moves us in different directions. Except for the fact that certain among us are under the notion that they can soak up speed into their limbs somehow.

Agree with you though, turning up hill allows the force of gravity to diminish kinetic energy. more potential is created if we move to higher height, and sliding back down due to accelerating forces of gravity allows potential energy to be converted back to motion, ie, kinetic energy...

Quote:

Originally Posted by

**Ghost**

Angular momentum L= IW, is also conserved (unless you apply a torque). You can move your cm closer to the axis of rotation. Say your new radius r, is r =R/2, in which case you will decrease rotational inertia From m R *R to m R/2 *R/2 = m(R^2)/4 your new w is now 4W so that your new angular momentum = (mr^2)w = (mR^2)/4 * (4W) = L = MR^2W as it was before.

Check.

Quote:

Originally Posted by

**Ghost**

Since the circumference of a circle is 2*pi*Radius, your old speed (if W was measured in rotations per second; if not, throw the a constant (k) into both equations) was W * 2*Pi*R m/s ; you new speed is w * 2 Pi r m/s = 4W * 2 * pi * R/2, or twice as fast.

Just to be clear, rotations/per sec is twice as fast. The speed of a point traveling around the circumfrence is not twice as fast. Care to estimate the change in speed along the circumference? Just curious.

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Originally Posted by

**Ghost**

You have worked on the system pushing the mass in the same direction as the force, increasing the kinetic energy of rotation, 1/2 I W ^2 and the velocity. You do have to push though.

Exactly

Moving part of the mass in or out, or rather changing the way the mass is distributed towards or away from the axis of rotation is called changing the "moment of inertia". If you want to imagine that the skier object is part of a larger mass where the skier is near the edge of the mass and the middle of the mass around the axis of rotation has zero mass...then ok...moving the skier towards the middle would be changing the moment of inertia and by conservation of momentum, the angular velocity would increase.

*However I question whether you can really consider a skier on a round turn to be an object with any angular momentum at all. Might be able to academically use the math to generate some interesting numbers but in practical terms, the skier does not have angular momentum, it has linear momemtum that is being constantly accelerated in a new direction by centripetal forces. that is different then say a spinning top which sits there and spins without any additional forces to keep it going. It thusly has angular momentum. *

Remove the external forces and a skier will go in a straight direction....ie...linear momentum.

As Lind stated in his text, pushing in a direction opposite of the centrifugal force vector is needed to move the mass inwards. Pushing against something, which in a ski turn is the ski edges and centripetal forces there. But... Be careful here, Lind did not equate this to a change in the moment of inertia and a conservation of momentum. He did refer to angular velocity, but he was also careful to point out that the radius is constantly changing throughout a turn, but in any case, he referred mainly to the fact that centrifugal force is present and by pushing against centrifugal force, more work is injected into the system and that equates to accelerating force, hopefully in a forward direction if that is what you want, but potentially turning you in a new direction too.

He states that muscle output generates force which provides acceleration, contributes work, he speaks in terms of angular velocity increasing here yes. If he were speaking in terms of angular momentum he would have to say that angular momentum is not only conserved by increased. But he did not refer to angular momentum and nor do I feel that angular momentum is increased unless the push off or pump creates rotation, in other words, is a form of torque.

Quote:

Originally Posted by

**Ghost**

On the other hand if you let the mass move to a larger radius, speed decreases, and decreases more if you resist the motion the way out there; your doing negative work on the system, and we are not in a purely rotational system.

Definitely we are not in a purely rotational system. I will argue that we are not in ANY rotational system in terms of the turn shape. If the skier itself is spinning a bit, like the way the earth spins while it goes around the sun, then that would be the measurable angular momentum present in a skier. The larger radius of the ski turn is not a self contained system, unlike the earth and sun which are attached to each other by gravity. A skier will not continue on any curved path at all unless continually acted upon by external forces in the right away, otherwise a skier will go straight. That is linear momentum.

The concept of doing negative work is also academic. Our muscles can't do negative work. We can do zero work and we can work, we can't do negative work. That's why we can't suck the speed into us. We can only find a way to do more work that goes in the opposite direction of whatever momentum we have established in order to have slowing effects, angular or linear, on the system.