Applications of uniform circular motion

A road turn

When a car takes a turn at constant speed, the road traces an arc of a circle. The necessary centripetal force is provided by the friction of the tires on the road (and by the banking of the track surface on circuits). If the speed is too high for the radius of the turn, the available friction is no longer sufficient: the car skids towards the outside of the turn.

A satellite in orbit

For a satellite in circular orbit around the Earth, it is the force of gravitation that plays the role of centripetal force. By equating the expression for gravitation to m*v^2/R, we can calculate the speed needed to maintain an orbit at a given altitude.

Some orders of magnitude

Situation	Radius R	Approx. speed v	Role of the centripetal force
Merry-go-round	3-8 m	2-5 m/s	Tension in chains/arms
Road turn	50-200 m	10-30 m/s	Tire/road friction
Low satellite (ISS)	~6800 km	~7.7 km/s	Earth's gravitation

Spinning laundry

In the drum of a washing machine, the laundry is pressed against the wall as it spins rapidly: the wall exerts on the laundry the necessary centripetal force, while the water, less constrained, escapes through the holes in the drum (it continues in a straight line, by inertia, as soon as it is no longer constrained).

Classic pitfall: it is not a force that "drives" the water outward; on the contrary, it is the lack of sufficient centripetal force on the water that makes it continue in a straight line (principle of inertia), until it exits through the holes.