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

DESCRIPTION: Attach a mounting frame to a variable speed rotator with the length of the pendulum of 10 cm. Adjust the rotation rate to less than about 1.6 revolutions per second, and the bob will remain in stable equilibrium in the vertical position. For rotational rates greater than 1.6 revolutions per second, the stable equilibrium position of the bob will be non-zero, depending on the rotation rate. For angular speeds greater than 2 or 3 revolutions per second the pendulum is erratic. For angular speeds less than about 3 revolutions per second the presence of a non-zero stable equilibrium position is readily demonstrated. Adjusting the length of the pendulum will change the critical angular speed.

SUGGESTIONS: Demonstration D5-23: ROTATING BEAD ON LOOP 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: Adjustable length pendulum in frame, motor, vibration absorbing base.

SETUP TIME: 10 min.

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