the carnival ride the \"gravitron\" you become stuck to the wall as the gravitro

Question

the carnival ride the "gravitron" you become stuck to the wall as the gravitron rotates. The angle between the floor and the wall is 110 deg. The wall has a coefficient of static friction of 0.7. The distance to the axis of rotation to the wall is 3m. What must the gravitron's angular velocity be in order to keep a 100kg person from sliding vertically down the wall

Explanation / Answer

let the normal reaction from the wall to the man be F. to prevent the man from sliding; mg*sin(180-110) = u*F => F = 100*9.8*sin(180-110)/0.7 = 1315.57 N now, computing for centripetal force ; F - mg cos(180-110) = mw^2*r => 1315.57 - 100*9.8*cos70 = 100*w^2*3 => w = 1.808 rad/s

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