Figure shows a car moving in a circular path with constant linear speed v. Such motion is called uniform circular motion. Because the car’s direction of motion changes, the car has an acceleration. For any motion, the velocity vector is tangent to the path. Consequently, when an object moves in a circular path, its velocity vector is perpendicular to the radius of the circle. We now show that the acceleration vector in uniform circular motion is always perpendicular to the path and always points toward the center of the circle.

Acceleration of this nature is called a centripetal(center-seeking) acceleration, and its magnitude is where r is the radius of the circle and the notation ar is used to indicate that the centripetal acceleration is along the radial direction.

Now let us consider a particle moving along a curved path where the velocity changes both in direction and in magnitude, as shown in Figure 4.17. As is always the case, the velocity vector is tangent to the path, but now the direction of the acceleration vector achanges from point to point. This vector can be resolved into two component vectors: a radial component vector ar and a tangential component vector at. Thus, a can be written as the vector sum of these component vectors: