An amusement park ride has a vertical cylinder with an inner radius of 3.7 m, wh

Question

An amusement park ride has a vertical cylinder with an inner radius of 3.7 m, which rotates about its vertical axis. Riders stand inside against the carpeted surface and rotate with the cylinder while it accelerates to its full angular velocity. At that point the floor drops away and friction between the riders and the cylinder prevents them from sliding downward. The coefficient of static friction between the riders and the cylinder is 0.9. What minimum angular velocity in radians/second is necessary to assure that the riders will not slide down the wall?

Explanation / Answer

Here,

r = 3.7 m

u = 0.90

let the angular speed needed is w

Now, as Normal force = centripetal force

N = m * w^2 * r

for the person to not slip

m * g = u * N

m * g = u * m * w^2 * r

9.80 = 0.90 * w^2 * 3.7

w = 1.72 rad/s

the minimum angular speed needed is 1.72 rad/s

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