Circular Motion & Gravitation

A car rounds a flat curve of radius 50 m. The coefficient of friction between tires and road is 0.4, g = 10 m/s². What is the maximum speed without skidding?

An amusement park ride consists of a circular, horizontal room. A rider leans against its frictionless outer walls, which are angled back at 30° with respect to the vertical, so that the rider's center of mass is 5.0 m from the center of the room. When the room begins to spin about its center, at what angular velocity will the rider's feet first lift off the floor?