You have been charged with operating "the gravitron" at the carnival. In this popular amusement ride, the entire ride spins with nauseous fairgoers leaning against the outside wall. When the requisite speed is reached, the floor opens up with the riders (red box in diagram below) pinned against the wall. You know that the ride has radius of R = 4.8 m (from center axis to rider's position), a wall angle θ = 25 reclined from vertical, and a coefficient of static friction μs = 0.24 between the rider and the wall.
What minimum rotation speed should you reach before dropping the floor?
