One popular ride at carnivals is the Roundabout, which works in the following manner. Riders stand on the inside edge of a circle, with their backs against a wall mounted on the edge of the circle. The wheel begins to spin. Once it is spinning fast enough the whole wheel tilts until the plane of the wheel is vertical (see picture). If the radius of the wheel is 8 meters, what angular velocity must the wheel have in rad/s so people don't fall off the wheel?

Answer 1

Let ω=angular velocity (rad/s)

To offset gravity, the centripetal force must offset gravity, g, or
rω²=g

Solve for ω.

Answer 2

1.106