a 70 kg man stands in contact against a wall of a cylindrical drum of radius 3 m rotating about its vertical axis with 200 rpm. 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? please explain it with diagram.

The man is standing in contact with the wall as shown below.

 

 

The normal reaction N provides the necessary centripetal force

 

N = mv²/r = mrω²

 

The frictional force balances the weight of the man

 

f_s = mg

 

Now, the man will remain stuck to the wall after the floor has been removed when

 

fs ≤ μ N

 

That is,

 

mg ≤ μ N

 

mg ≤ μmrω²

 

ω² ≥ g/μr

 

Thus, the minimum rotational speed is