Circular Motion

In circular motion the velocity is always changing, because its direction turns even when its speed does not. That change is an acceleration pointing to the center, the centripetal acceleration a_c = v²/r. By Newton’s second law something must supply the matching inward force, and the radial forces add up to ΣF_r = m·v²/r. When the speed is steady, that radial force is the whole net force; when the speed also changes, a tangential force acts alongside it. That force is never a new kind of force. It is the role played by whatever real force already acts: the tension in a string, gravity on a satellite, the normal force from a track, the friction under a turning car.

Three pictures get drawn wrong. Sketching centripetal force as a separate arrow, an extra force beside the real ones, when the inward force is one of those real forces, not a second one. Inventing an outward centrifugal force in the ground frame, when no outward force acts on an object rounding a curve — the feeling of being flung outward is inertia, not a force. And reading constant speed as zero acceleration, when the speed can hold steady while the velocity's direction keeps turning, so the acceleration is v²/r inward and never zero.