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. 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?
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. 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?

m = 70 kg m

The drum’s radius is 3 metres.

= 0.15 is the coefficient of friction between the wall and his clothes.

The number of revolutions per minute of a hollow cylindrical drum is 200/60 = 10/3 revolutions per second.

The normal N of the wall on the guy provides the needed centripetal force.

mv2/R = m2R N = mv2/R = m2R

The guy adheres to the drum’s wall while the floor spins. As a result, the frictional force acting vertically upwards balances the weight of the man (mg) acting downward.

If mg limits frictional force fe (N), the guy will not fall.

mg ≤ μN

mg ≤ μ (mω2R)

ω2 ≥ g/Rμg

As a result, given the cylinder’s minimum rotational speed,

ω2 = g/Rμ = 10/(0.15 x 3) = 22. 2

ω =√22.2 = 4.7 rad