Problem 1.286

A uniform sphere of mass \(m=5.0 \mathrm{~kg}\) and radius \(R\) \(=6.0 \mathrm{~cm}\) rotates with an angular velocity \(\omega=1250 \mathrm{rad} / \mathrm{s}\) about a horizontal axle passing through its centre and fixed on the mounting base by means of bearings. The distance between the bearings equals \(l=15 \mathrm{~cm} .\) The base is set in rotation about a vertical axis with an angular velocity \(\omega^{\prime}=5.0 \mathrm{rad} / \mathrm{s}\). Find the modulus and \(\mathrm{di}\) rection of the gyroscopic forces.