| Yes, they do.  However, skaters are trained to immediately pick a fixed point in the horizion upon cessation of the spin (ie, staring at something fixed) which helps them regain their balance and sense of motion. 
				__________________"I've made only one mistake in my life.  But I made it over and over and over.  That was saying 'yes' when I meant 'no'.  Forgive me."
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