In some amusement parks there is a ride which is effectively a hallow cylinder which can rotate about its vertical axis. The riders stand on horizontal base of the cylinder and in contact with the curved surface of the cylinder. When the angular speed reaches a certain value the floor is dropped but the riders remain in contact with the curved surface of the cylinder. The radius of the cylinder is 2.5m, and the speed of rotation is 30 revolutions per minute.
How do I draw the forces acting on this cylinder if people are modelled as a particle?
And how do I find the smallest possible coefficient of friction between the rider and the cylinder surface so that the ride works effectively?
I found the velocity but where do I go from here?
Let $\omega$ be the angular speed so$$\omega=\frac{30\times2\pi}{60}$$ radians per second
Draw the normal reaction $N$ horizontally in the same direction as the acceleration $r\omega^2$. The limiting friction is $\mu N$ acting vertically upwards, and the weight is $mg$ vertically downwards.
So you then have $$\mu N=mg$$ and $$N=mr\omega^2$$
So you can solve to get $\mu$