Answer
μs = 0.18
Work Step by Step
Variable list
f is friction, m is mass, a is acceleration, V is velocity, r is radius, W is weight, n is normal force, T is time, g is gravitation acceleration on Earth, and μ is the coefficient of static friction.
First draw a free-body diagram of the person riding on the "Rotor-ride"
Second write a summation of forces statement for forces in the X direction.
ΣFx: n = ma
n = mV^2/r
Third write a summation of forces statement for forces in the Y direction.
ΣFy: f - W = ma Since there is zero acceleration, "ma" cancels out.
f = W
Add W.
μn = mg
Divide by n.
μ = mg/n
μ = mg/mV^2/r
Divide by m.
μ = g/V^2/r
μ = g/(2πr/T)^2 /r
Substitute in the equation for velocity.
μ = g/4π² r^2/T^2/r
Divide by r.
μ = g/4π² r/T^2
μ = gT^2/4π² r
μ = (9.8m/s^2)(2s)^2/4π² (5.5)
Since there is 0.5 revolutions per second, the total time period would be 2 seconds. Time period measures how much time it takes to complete one revolution in how many seconds. 0.5 revolutions per second times 2 equals 1 revolution in 2 seconds.
μ = 0.18