Final answer:
The acceleration vector of a particle in circular motion consists of tangential acceleration, which changes the particle's speed, and radial (centripetal) acceleration, which changes its direction and keeps it in circular motion. The acceleration vector is the sum of these components, which are perpendicular to each other.
Step-by-step explanation:
The acceleration vector of a particle moving in a circular path can be decomposed into two perpendicular components: the tangential acceleration and the radial (or centripetal) acceleration. The tangential acceleration is in the direction tangent to the circle at the particle's location and is responsible for changing the speed of the particle along its path. On the other hand, the radial acceleration points toward the center of the circle and is responsible for changing the direction of the velocity vector, keeping the particle in circular motion. This radial acceleration is also known as centripetal acceleration. It's important to note that velocity can also be decomposed similarly; for instance, when a particle is in uniform circular motion, its velocity vector is always perpendicular to the radius vector of the circle. The acceleration vector is the sum of the tangential and radial (centripetal) accelerations and points at an angle between them.