The inward pull that sustains circular paths
An object moving in a circle experiences constant acceleration toward the center, even at constant speed, because its velocity direction continuously changes. This acceleration requires a force, the centripetal force, directed inward. For a satellite orbiting Earth, gravity provides the centripetal force. For a car rounding a curve, friction supplies it. Without centripetal force, the object flies off tangentially.
The magnitude of required centripetal force is F = mv^2/r: it increases with mass and the square of velocity, and decreases with radius. Doubling speed requires four times the force. This explains why high-speed turns need greater lean angles in motorcycles or banking in racetracks. The centripetal acceleration is purely directional, not about speeding up or slowing down.
Real forces masquerading as centrifugal effects
A common misconception treats centrifugal force as real, pulling outward. It isn't; it's a fictitious force that appears only in rotating reference frames. When you sit in a car turning left, you feel pushed right, not because of a real outward force, but because your body tends straight (Newton's first law) while the car turns left. An inertial observer sees only the real centripetal force turning you with the car.
This distinction matters in orbital mechanics and rotating machinery. In the Earth's reference frame (rotating), objects experience fictitious centrifugal and Coriolis forces. These calculations work for practical problems, but they're artifacts of our frame choice, not fundamental forces. Real centripetal forces, by contrast, are effects of actual interactions: gravity, friction, or tension pulling inward.