Worksheet: Gyroscopic Precession

In this worksheet, we will practice calculating the precession angular velocity of a gyroscope given its mass, radius, and rate of revolution.

Q1:

A gyroscope has a disk of mass 5 . 0 × 1 0 2 g and radius 0.100 m. The disk spins at 40 rev/s. The center of mass of the disk is 0.10 m from a pivot. What is the precession angular velocity of the gyroscope?

Q2:

The precession angular velocity of a gyroscope is 2.5 rad/s. The mass of the rotating disk is 0.82 kg and it has a radius of 50.0 cm. The distance from the center of mass to the pivot is also 50.0 cm. What is the rotation rate of the disk?

Q3:

A gyroscopically spinning top has a precession frequency of 5.0 rad/s on Earth. If the spinning top was used on the Moon, what would its precessional frequency be?

Q4:

A gyroscope spins with its tip on the ground which produces negligible frictional resistance. The gyroscope disk has a radius of 5.0 cm and a mass of 0.30 kg and spins at 20 rev/s. The center of mass of the gyroscope’s disk is at a 5.0 cm displacement from its tip along the rotational axis of the gyroscope. What is the precessional period of the gyroscope?

Q5:

A spinning top has a moment of inertia 2 . 3 × 1 0 4 kg⋅m2 and a radius of 5.00 cm from the center of mass to the pivot point. The top spins at 33 rev/s and it is precessing. Through how many revolutions does the top precess in 12 s?

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