Final answer:
The force on a particle in circular motion can be along the radial vector as centripetal force or along the tangent vector as tangential force. Centripetal force is 'center-seeking' and directed radially inward, while tangential force affects the particle's speed along the path.
Step-by-step explanation:
The force on a particle in motion can be directed along different vectors depending on the circumstances of the motion. When we consider a particle in circular motion, there are two primary forces to consider: centripetal force and tangential force. The centripetal force is directed along the radial vector towards the center of the circular path as this force is what keeps the particle moving in a circle hence why it is referred to as 'center-seeking'.
This force is responsible for the centripetal acceleration of the particle and is always directed radially inward. On the other hand, tangential force affects the particle's speed along its path and is directed along the tangent vector which is perpendicular to the radius at the point of the particle's location in its circular path.