Cycloid | Kinematics representation

In this animation, we can observe the trajectory traced by a point on a circle as it rolls along a straight line without slipping. This curve is known as a cycloid. When considering a constant translational speed of the circle, we analyze the time rate of change of the vector position, resulting in the velocity vector that is always tangent to this trajectory. Additionally, the acceleration vector always points toward the center of the circle because the only acceleration present at any point on the circle is the centripetal acceleration.