# Physics of the point of contact for a spinning top

I understand how spinning tops don't tip over, cf. e.g. this and this Phys.SE questions. What I'm more interested is in identifying the factors that determine the direction the spinning top moves to?

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I would imagine that has something to do with the initial velocity you give it when you set it in motion (i.e. when you set the top in motion, you apply both torque and force, changing both angular and linear momentum of the top). The point of contact would move straight along the surface and also rotate (though how exactly a point can 'rotate' I'm not sure). The interaction between the spinning top and surface no doubt creates some friction which would determine how the spinning top moves (it would also explain how the top loses energy to eventually topple over). – Greg May 15 '13 at 6:50
As Greg, I am pretty sure the movement is determined by the irregularities (and initial velocity of the top) of the surface. If you were to put an ideal pointy top on a perfectly smooth surface, there is no reason for it to move in any direction – Mathusalem May 15 '13 at 7:56

It depends on the friction of the contact. With a frictionless plane the top would precess around its center of gravity and the contact point will prescribe a circle.

Add friction, and the friction force translates the center of gravity the same way tire traction translates a car. Here you have the cases of a) pure rolling, or b) rolling with slipping.

With pure rolling the motion is similar to a spinning coin rolling on its edge, or a spinning glass which precesses in a circle smaller than the contact ball radius.

With slipping there isn't enough force for such a tight circle, so the precession yields wide circles that become progressively smaller and smaller.

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