Static and Dynamical System Equilibrium

Look at the picture below - what do you see ?

This is a toy called a Levitron. The "anti-gravity" force that repels the top from the base is magnetism.

To prevent the top from overturning, as well as provide a force on the top as a whole, the magnetic field of the base gives a torque tending to turn the top towards its axis of spin. If the top were NOT spinning, this magnetic torque would turn it over.

The top spins in the range from about 20 to 26 revolutions per second (rps). It is completely unstable above 30 rps and below 18 rps.

Many dynamical systems display this type of property - stable ONLY within specific ranges of rotation and/or vibration.

The same principle is observed in a toy called the "inverting top"

The "inverting top" is another child's toy which shows the difference between dynamic and static stability and balances in an improbable manner.

However in this toy there is no magnets to hold the system in place.

If you look at centre of gravity in the picture above you can see that it is too high for this toy to balance easily. Imagine a pencil balanced on its point and you have a very similar type of instability.

This picture was taken with a slower shutter speed - you can see that the top is spinning (note that the wooden floor is in focus).

This system is stable in one configuration while spinning, but at rest it is stable in two different configurations.

The following photographs are of the toy at rest - in its natural, non-dynamic, stable states.

The static equilibrium condition of the top is on its base or side.

The dynamically stable state of the spinning top is inverted, it spins on it's point.

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