A `70kg` man stands in contact against the inner wall of a hollow cylindrical drum of radius `3m` rotating about its verticle axis. The coefficient of friction between the wall and his clothing is `0.15` . 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

Here, `m = 70 kg, r = 3`.
`omega = 200 "rpm" = (200)/(60) rps = (10)/(3) xx 2pi rad//s`
In the present case, necessary centripetal force is provided by the horizontal rection `H` of the wall on the man, i.e.,
`H = (m upsilon^(2))/(r ) = m r omega^(2) ( :' upsilon = r omega)`
The frictional force `F` acts upwards and balance the weight `mg` of the man.
The man will remain stuck to the wall after the floor is remved, if weight of man `le "force" o` friction
or `mg le mu H(= mu m r omega^(2))`
or `(g)/(mu r) le omega^(2) or omega^(2) ge (g)/(mu r)`
`:. omega_(min) = sqrt((g)/(mu r)) = sqrt((9.8)/(0.15 xx 3)) = 4.67 rad//sec`.