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A demonstration gyroscope consists of a uniform disk with a 40.0-cm radius, mounted at the...

A demonstration gyroscope consists of a uniform disk with a 40.0-cm radius, mounted at the midpoint of a light 60.0-cm axle. The axle is supported at one end while in a horizontal position. How fast is the gyroscope precessing, in units of rad/s, if the disk is spinning around the axle at 30.0 rev/s?

Step-by-Step Solution

Solution 1
Step #1 of 7

THINK:

Step #2 of 7

Determine the precessional angular speed of the gyroscope, in units of rad/s.

Step #3 of 7

SKETCH:

The figure shows the precessional motion of a demonstration gyroscope.

Step #4 of 7

RESEARCH:

The expression for the precessional angular speed is given by

The moment of inertia of the disk of mass and radius is given by

Step #5 of 7

SIMPLIFY:

From the diagram,

The angular speed of precession of the gyroscope is given by

Step #6 of 7

GIVEN DATA:

Radius of the uniform disk,

The angular speed of the disk,

Length of the axle,

Acceleration due to gravity,

Step #7 of 7

CALCULATE:

The precessional angular speed of the gyroscope is given by

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