A popular carnival ride consists of a large, round room that rotates fast enough

Question

A popular carnival ride consists of a large, round room that rotates fast enough that any person standing against the wall will be stuck there, even as the floor is dropped away from their feet. The coefficient of static friction between the person and the wall is ?s, and the radius of the cylinder is R. a) Find an equation for the minimum period of rotation, T, needed to keep the people in place on the wall. This equation will include ?s, R, g and ?. b) Solve for T if R = 4.00 m and ?s = 0.60. What is the room's angular speed in rpm?

Explanation / Answer

Writing statics equations:

N = mrw^2

friction f = N = mg

SO we have   rw^2 = g ie w= sqrt(g/ r)

a) T = 2/w = 2 (r/g)

b)  w= sqrt(g/ r) = sqrt(9.81/0.6*4) = 2.0218 s^-1

Hope you like my detailed explanation :)

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