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A Tippy-Top, having a section of a spherical surface of large radius on one end and a stem for spinning it on the opposite end, will rest on its spherical surface with no spin but slips over when spun, so as to stand on its stem. Explain. (See "The Tippy-Top," by George D. Freier, The Physics Teacher; January 1967, p. 36.) If you cannot find a Tippy-Top, use a hard- boiled egg; the "standing-on-end" behavior of the spinning egg is most easily followed if you put an ink mark on the "pointed" end of the egg.

A Tippy-Top, having a section of a spherical surface of large radius on one end and a stem for spinning it on the opposite end, will rest on its spherical surface with no spin but slips over when spun, so as to stand on its stem. Explain. (See "The Tippy-Top," by George D. Freier, The Physics Teacher; January 1967, p. 36.) If you cannot find a Tippy-Top, use a hard- boiled egg; the "standing-on-end"  behavior of the spinning egg is most easily followed if you put an ink mark on the "pointed" end of the egg.

Grade:upto college level

1 Answers

Deepak Patra
askIITians Faculty 471 Points
6 years ago
The figure below shows the Tippy-top in the initial position, when it is given the angular speed ωbeg.


233-2358_1.PNG
It can be seen from the figure above that the point of curvature (CC) of the tippy top lies above the center of gravity (CG). This ensures the initial stability of the tippy top. But as soon as some angular speed is imparted, the center of gravity (CG) moves away from the center of curvature such that the gravitational force of the tippy top exert a torque on it (refer figure below).
233-2298_1.PNG
It can be seen from the figure above that the force acts on the tippy toy, passes through the center of gravity and exerts a torque on it thereby rotating it in counterclockwise direction.
As the tippy top fall over and over with shift in center of gravity (CG), it will eventually touch the ground and experiences frictional forces. The frictional force say f between the tip of the tippy top and the ground exerts a torque on it, trying to impart the angular velocity in the direction coming out of the plane of paper (as shown below).
233-2352_1.PNG
Since the torque on the top of the tippy toy rotates about the same point and stands on its tip. It is important to note that the fictional force is responsible for raising the center of curvature (CC) and center of gravity (CG).
The friction between the surface and the top of the toppy top has increased the potential energy of the top but at a loss of kinetic energy (as shown in figure below).
233-1534_1.PNG
The figure above shows the final position of the tippy top, rotating with angular speed ωend.

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