@Loki1, I've been thinking about this a bit more, and anticipating that you are interested in how the skis change from pointing down the fall line to pointing across the hill. Are there any absolutes?
1. Differences between outside ski and inside ski can't be absolutes because White Pass turns can be done, as well as one-ski skiing.
2. That change can happen without any rotational momentum that was started by the skier when the skis were moving across the hill above the fall line. We know the skier can start with skis pointing down the fall line and end with skis going across the hill. So rotational momentum, or initial steering angle, started back up in the top of the turn, or during transition, is not an absolute necessity for getting skis to go the other way along a curved path.
3. So let's look at how the skier can get that curved path to happen while the skis are pointing and going down the fall line.
.........Roll ankles/knees, or angulate at the hip. This tips the skis onto uphill edges, they bend because of how the skis are shaped, a platform is formed on the snow, and the snow pushes the skis along a curved path across the hill. So snow platform and centripetal force is at work. Is this an absolute? Not willing to go there yet.
.........Rotate upper body to face the side of the trail; this rotation will drag flat-ish skis, or lightened skis, around and take the skier across the hill along a curved path. Do the skis have to be tipped onto uphill edges as they move across the snow, even a little, while the upper body is rotating for this to work? Since the skiers doing this are aft, and often leaning in, the tails of skis in this instance get displaced outward and that's not going to happen unless they are on uphill edges. So let's say yes, an ungripping snow platform and some resulting centripetal force are at least present, if not dominant in causing the curved path across the hill. Still not willing to say centripetal force is an absolute.
.........Ron LeMaster talks about the differential steering angle in the shovel vs the tail of an edged ski. That difference accompanies both of the examples I've given and happens even if the skier is aft. See his book for a detailed description. Is this steering angle that's inherent to a bent ski, its "self-steering" function, an absolute? If centripetal force is always present, then this is always present. Still not ready to call these absolutes.
........These things listed above assume the skis are moving downhill at the start. Is forward linear momentum necessary for the skis to turn (and contributing to that turning)? No, because the skier can hop to an edge from a static start (Hop Turns, which count as turns in PSIA manuals).
........Here's the one type of turn I've waited to talk about that gives me pause in finding anything to be an
absolute. Slide downhill on flat skis. Slide one foot back relative to the other, using hamstrings, so that hips do not turn. Skis will turn to the side of the pulled-back foot/ski and take the skier along a curved path across the hill. My eyes are not down there at snow level; does this pull-back movement of what ends up being the inside ski tip it? If yes, then a bit of platform happens and we've got centripetal force at work. But I'm not sure the skis tip. I do 360º spins this way. I work to keep the skis flat. The pull-back move, plus gained rotational momentum, makes those spins work. Not tipped and edged skis. If it's something other than snow platform pushing on a bent ski that makes this pull-back work, that is, if it happens with both skis staying flat, then centripetal force and differential steering angle within the ski are not in play. If they are not in play in this one instance, then they are not absolutes.
--The way this turn might happen with skis staying flat is similar to how a tank or snow groomer turns. The rotating track on one side pulls against the snow one way and the other tracks pulls against the snow the other way. The machine turns. Look up force-couple for an engineering description of how this works.
--Does the bottom of a ski have grip, even if it's not edged, which would allow the force-couple phenomenon to work? Is there enough grip or friction between the base of the pulled-back inside ski to turn the skier like a tank turns when going slow on low pitch terrain? Is there enough grip/friction to start the skier spinning around in 360ºs on truly flat skis without relying on edging, bending, self-steering, and centripetal force? I think so. I can't see the snow-surface and ski's base to really
know. Maybe. If so, then there are no absolutes for making the skis turn from downhill to across the hill, none at all. There are numbers of ways of getting the skis to turn, not just one.
Back to your question. There's not one thing that absolutely has to happen
back up in transition, that's a certainty for all turns everywhere, because turns can start at the fall line from a straight run.
), left accelerating force becomes right accelerating force. It is well known that (aka too lazy to support it with proof or reference -be thankful I'm not using proof by reductio ad nauseum) tipped skis apply forces, therefore left tipped ski becomes right tipped ski, or if skiing in a wedge with opposing edges, dominant edge (due to weight and angle) changes.
