Quote:

**Can someone please address this question? Thanks!** |

Well, I'll try, Lisamarie! Fox's question is a great one. Unfortunately, it's a little like asking "can someone please explain physics for me"! As Fox says, "it's rocket science," and I'm not a rocket scientist either. If we're lucky, PhysicsMan himself may find time to jump in here. Meanwhile, I'll do my best.

Fox--your observation is entirely correct, but as Einstein said, Newton's physics, while not wrong, need supplementation to explain things like "centrifugal force," a force that "does not exist" in some analysis, but that we skiers can certainly vouch for!

Centrifugal force is that very obvious force we feel and react to, pulling us sideways, out of the turn. It increases with speed and with decreasing turn radius, and in many turns it is the primary force we deal with for balance. (Gravity is the other main force we must add to the balance equation.)

Yet, by Newton's laws, centrifugal force does not exist! Newton says (correctly, of course) that if we are TURNING (turns are a form of changing motion, or acceleration), then the combination of all forces acting on us is pulling/pushing us INTO the turn. Yet we feel "centrifugal force" pulling us OUT of the turn. And we clearly balance against its pull by leaning INTO the turn. How can this be?

The answer lies in understanding the relativity of motion--things move only in relation to other things, and there is no such thing as "pure motion." In other words, when we say we're driving "west at 60 mph," we have to recognize that that is a very relative speed and direction. It's 60 mph relative to the surface of the earth, but we're travelling a very different speed and direction around the sun, and another speed and direction around the earth's axis as it rotates to the east. Even so, the person asleep in the passenger seat isn't moving at all!

How can this be? We discussed this exact point recently in another thread, appropriately entitled,:

The Paradox of Skiing. It's a question of perspective. From your perspective ("frame of reference") in the car, you and your passenger are sitting still, not moving. In that case, according to Newton's Laws, there must be no "net force" acting on you--you are "a body at rest." You are at "equilibrium"--you are IN BALANCE. Centrifugal force pulls you sideways when the car goes around a curve, and you feel the car (seat/door/whatever) pushing you the other way with the same ("equal and opposite") force. The combination of forces "net force") equals zero, and you remain right that there, unmoving, in your seat.

An observer at the roadside would have an entirely different awareness of the situation. From his perspective, you are NOT sitting still in one place--you are travelling around a curve, at 60 mph! From his perspective, of course, you are NOT at "equilibrium"--there is a significant net force acting on you, pushing you around that curve, and you are therefore NOT "in balance." But his perspective is NOT yours, is it? The one that matters to YOU is YOUR frame of reference, in which you are sitting still and your passenger is asleep, motionless! From the bystander's perspective, at one moment you are "over there," and at another, you are somewhere else. From your perspective, you are ALWAYS "right here."

So, back to Fox's question.... From the bystander's frame of reference, the skier making turns (direction changes) down the hill is NOT in equilibrium/balance--there are non-zero net forces acting almost constantly, from constantly changing directions, constantly altering the skier's path. From the skier's perspective, though, he is always "right here," and to remain that way, he must remain in balance--at equilibrium. If he is in "balance," then there is NO NET FORCE--"horizontal" or otherwise--acting on him! Centrifugal force, gravity, and the forces of the snow and wind pushing on him all combine to equal exactly ZERO. From his perspective ONLY, the skier is in "dynamic balance."

(And Centrifugal Force, from his perspective, is VERY real!)

Here's another possible way to look at the "horizontal forces" thing. Again, from your perspective, you are in "dynamic balance," and you "job" is to keep it that way, in order to avoid falling down. When you stand on two feet, you can literally PUSH yourself left and right by pressing on one foot or the other. If you plant a pole to the side, you can push sideways even harder. And if you use those long skis and stiff boots, you can push yourself forward and back as well. There are many "horizontal forces" you can introduce, pushing your body (center of mass) laterally and fore-aft, and helping to recover when knocked off balance, and providing a large stable platform when standing still (static balance). Now imagine riding a bicycle, or better yet, a unicycle. Imagine standing still. From that one-point unicycle stance, you can NOT push yourself sideways. If you aren't in balance, you fall over. When moving, to make a turn, you cannot just "transfer your weight" and push yourself sideways in the new direction (you could if you had poles, but you don't). Your balance depends entirely on the relationship between your center of mass and the point of contact of the wheel. Being in balance requires "leaning forward" of the wheel when gaining speed, "leaning back" when braking, and leaning precisely the right amount into every turn. You cannot introduce any "horizontal" forces on your center of mass, but you CAN introduce them to the wheel--you can pedal harder to accelerate it forward (of YOU), brake to move it "back," and turn it to move it "sideways." You can move the point of contact in relation to your CM, but you cannot muscularly move your CM in relation to the point of contact--because you cannot directly create "horizontal forces" on your CM.

To remain "in balance" on a unicycle, you must move the wheel around beneath you such that the line between the point of contact and your center of mass (the "line of action") tips at precisely the right angle to keep all the forces at equilibrium. When standing still, the line must be vertical. When turning, the line leans into the turn. When gaining speed, the line tips forward, and when braking, the line tips backward. Or else you fall! Ironically, because you can't directly "push" your CM around on a unicycle, "braking" requires first pedaling faster to the get the wheel in front of you. "Accelerating" (going faster) requires first BRAKING to get the wheel behind you. And going right requires first turning left to get the wheel to your left.

On skis, things are different. From an open stance, you can move your CM laterally just by shifting your weight, and you can push yourself forward and back, levering from those long skis, through your stiff boots, and you can push yourself around with your poles.

*This is NOT to say that you SHOULD do these things, necessarily; only that you CAN, when you NEED to!* Great, flowing, "balanced" skiing works more like the unicycle, where the skier remains centered, in balance over a single "point of contact" that moves smoothly and continuously along your chosen path down the hill. "Out of balance" skiers are the ones who must use their "horizontal force creating ability" frequently and grossly, to keep from falling down.

Aren't you glad you asked, Lisamarie? Great queston, Fox!

Best regards,

Bob Barnes

[ December 04, 2002, 09:20 AM: Message edited by: Bob Barnes/Colorado ]