@ly9nd

5 months ago

No offense, but I believe you are confused between various different things.

Lean does not make you go fast, rather lean is required to go fast around a curve, simply leaning won't do anything - this is why you will fall if you simply lean - skater has to actively turn to not fall when leaning or keep crossing over.

A skater will need to generate centripetal force to go in a curved path, that force does not come from the lean, it actually is generated by legs doing to crossover as skater keeps stepping inward ( and they actually will go tangentially if they stop doing crossover or if they stop actively trying to turn with the ankles ).

The reason lean is needed is so that centrifugal force won't topple over the skater.

The net torque in the frame of reference of the skater should be 0. assuming the lean to be theta with the vertical ( so 0 degree means 0 lean )

mv^2/r cos ( theta ) = mg sin ( theta )
tan ( theta ) = v^2/2rg

so the faster you go the more you need to lean otherwise you will be thrown out of the circle ( which will icrease r and reduce the theta ) or you will simply topple over.

The net force must also be balanced ( assuming 0 acceleration ), this is very complicated equation and simply saying centrifugal force = friction force would be incorrect as edges dig into the ice, and there are other force involved.

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