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I was gonna say hell no..but now that i think about it... On a technical level a symmetrical ski would have weight completely even on both sides of you, allowing you to spin cleaner and faster, while non-symmetrical skis would be slower.
Even if it does spin faster you probably wont notice it unless you have your bindings set far back...
dont think the weight would be that much of a difference, would be more worried about swing weight center vs true center, even at true center weight is still back of center because boot sole center and centermount do not place your weight in the middle of the ski....try balancing out your weight on a ski so it is exactly even that would be interesting
Yes, in theory the physics will say you will spin faster if the weight is distributed equally on both ends.. However on a non symmetrical park ski the weight displacement over the nose will be virtually unnoticeable, and your moment of inertia for you and your skis will be identical. If you mount 200cm skis 50cm back from center than you might be able to notice something haha, there's no difference man
I guess we're assuming that both skis are center mounted.
Non-symmetrical skis have a wider nose so they will be slightly nose-heavy. On the other hand the heel piece of your binding is usually heavier than the toe piece. The bindings are very close to the spinning axis though, so it's hard to say whether their weight will matter. A very interesting question.
In the real world none of this will make any difference though.