Horizontal Circular Motion

When an object moves in a horizontal circle at constant speed, it accelerates toward the center. By Newton's second law, a net force must cause this centripetal acceleration:

Here $m$ is the mass, $v$ is the speed, and $r$ is the radius of the circular path.

Example: A Car on a Flat Curve

Consider a car turning on a flat horizontal road. The friction between the tires and road provides the centripetal force:

The vertical forces—weight $mg$ downward and normal force $N$ upward—balance each other. They do not contribute to the horizontal motion. Only the friction force $f$ acts horizontally toward the center:

The free-body diagram shows all forces acting on the car: