Question

A certain gyroscope consists of uniform disk with a 50 cm radius mounted at the center of an axle that is 11 cm long and of negligible mass. The axle is horizontal and supported at one end. If the disk is spinning around the axle at 1000 rev/min, what is the precession rate?

Answer 1

The precession rate of a gyroscope is calculated by the torque due to gravity and the angular momentum of the spinning disk. Applying the formula for angular momentum (L) and torque (τ), the precession rate (ωp = τ/L) can be determined.

Step-by-step explanation:

To determine the precession rate of a gyroscope, we must apply the concept of angular momentum. The gyroscope described has a disk of 50 cm radius and it's spinning around an axle of 11 cm length at 1000 revolutions per minute (rpm). The precession rate is influenced by the torque due to gravity, the angular velocity of the spinning disk, and the moment of inertia of the disk.

The angular momentum (L) of a spinning object is given by L = Iω, where I is the moment of inertia and ω is the angular velocity. The torque (τ) caused by gravity on the gyroscope can be found by τ = rmg, where r is the distance from the pivot to the center of mass, m is the mass of the disk, and g is the acceleration due to gravity. The precession rate, or angular velocity of precession (ωp), occurs due to this torque and is given by ωp = τ/L.