Question

A given gyroscope is made from a uniform disk with a 50-cm radius mounted on an axle through the disk’s center that is 11 cm long through the disk’s center and has negligible mass. The axle is supported at the far end from the disk, and makes an angle of 30o above the horizontal. If the disk is spinning around the axle at 1000 rev/min, what is its rate of precession?

Answer 1

the rate of precession is 0.041 rad/s

Explanation:

given information:

radius, R = 50 cm= 0.5 m

disk length, d = 11 cm, r = 5.5 cm = 0.055

angle, θ = 30°

angular velocity of the disk, ω = 1000 rev/min = 1000 2π/60 =

rate precession, Ω

Ω = m g r / I ω

where

m = mass

g = gravitational force

r = the radius of the center disk

I = inertia

ω = angular veocity

I =
`(1)/(2) mR^(2)`

Ω = (m g r )/ (
`(1)/(2) mR^(2)` ω)

= 2 g r / (
`R^(2)` ω)

= 2 x 9.8 x 0.055 / (
`0.5^(2)` 104.7)

= 0.041 rad/s