Question

A cylindrical disc of a gyroscope of mass m = 15 kg and radius r = 5.0 cm spins with an angular velocity ω= 330 rad/. The distance between the bearings in which the axle of the disc is mounted is equal to l = 15 cm. The axle is forced to oscillate about a horizontal axis with a **** T = 1.0 and amplitude ϕm, = 20°. Find the maximum value of the gyroscopic forces exerted by the axle on the bearings.

Answer 1

The moment of inertia is 1/2mr2 and angular momentum is 1/2mr2ω.The axle oscillates about a horizontal axis making an instantaneous angle.

This means that there is a variable precession with a rate of precession d*ϕ/*dtThe maximum value of this is

When the angle between the axle and the axis is at its maximum value, a torque I*ω*Ω