Theoretical problems
Problem 1
A hollow sphere of radius R = 0.5 m rotates about a vertical axis through its centre with an angular velocity of ω = 5 s^-1. Inside the sphere a small block is moving together with the sphere at the height of R/2 (Fig. 6). (g = 10 m/s².)
a) What should be at least the coefficient of friction to fulfill this condition?
b) Find the minimal coefficient of friction also for the case of ω = 8 s^-1.
c) Investigate the problem of stability in both cases,
α) for a small change of the position of the block,
β) for a small change of the angular velocity of the