PURPOSE: To demonstrate the presence of a "critical parameter" which determines the dynamic behavior of a simple physical system.

DESCRIPTION: Attach the mounting frame to the variable speed rotator and adjust the rotation rate for less than 1.6 revolutions per second. The bead remains in equilibrium at the bottom of the loop. For rotational rates greater than 1.6 revolutions per second, the bead will be in stable equilibrium at a non-zero angle dependent on the rotation raate. Frictional effects are considerable; nevertheless the presence of a critical angular velocity can be seen.

SUGGESTIONS: Demonstration D5-22: ROTATING PENDULUM can be used in conjunction with this demonstration. Both systems are dynamically identical, exhibiting an effective potential whose shape is dependent on a single parameter, the rotational speed.

REFERENCES: (PIRA unavailable.) See Demonstration Reference File for further information, including theory.

EQUIPMENT: Bead on loop in frame, motor, vibration absorbing base.

SETUP TIME: 10 min.

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