A 70 kg man stands in contact against the inner wall of a hollow cylindrical drum of radius 3 m rotating about its vertical axis with 200 rev/min. The coefficient of friction between the wall and his clothing is 0.15 m What is the minimum rotational speed of the cylinder to enable the man to remain stuck to the wall (without falling) when the floor is suddenly removed ?

Explanation

The frictional force f (vertically upwards) opposes the weight mg. The man remains stuck to the wall after the floor is removed if
`mg le f_(L) i.e., mg lt mu m R omega^(2)`.
The minimum angular speed of rotation of the cylinder is
`omega_(min)=sqrt((g)/(mu R))=sqrt((9.8)/(0.15xx3))=4.67 s^(-1)`.