Curious case of the mystery top (i)
The tippe top toy is one of the great mysteries of science. As you see below, when it is set to spin with sufficient angular velocity, the top turns itself over and spins on its stem for a while until friction slows it down.
Suppose we draw an arrow on the upright tippe top, pointing counterclockwise, as so
If we spin the top counterclockwise (in the direction of the arrow), what will happen when the tippe top turns over to spin on its stem?
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The arrow is drawn to point counter-clockwise. In the initial spin (before flipping) the arrow points in the direction of the spin, as the imparted spin is counter-clockwise too. Finally when it flips over, the direction of spin is maintained by the top. But due to the flip the arrow's head will be pointing away from the direction of the spin. Ergo the arrow points away from the direction of the spin.