Centripetal force and centrifugal force are two terms that physics students commonly confuse or misunderstand.
A typical misconception is that centripetal force is directed toward the center of an object's circular path, while centrifugal force is directed outward, as though the two act in opposite directions. However, only one of these is actually a real force!
Centripetal vs. Centrifugal Force
The only force causing an object's circular motion is centripetal force, which is always directed toward the center of the circular path. If a car is rounding a bend, for example, the centripetal force making it move in a curve rather than a straight line is directed along the radius of the circle the car is tracing out.
Centrifugal force is a fictitious force, meaning that it is not a real force. Centripetal force is real.
Centrifugal force, on the other hand, does not exist. Like "Back to the Future's" flux capacitor, the term was invented to help describe something imaginary, albeit based on some real observations. The effects of moving in a circle tend to make an object feel like it is "flying" outward, and the idea of an inward-directed force causing such an experience can at first seem puzzling.
Centrifugal Force Is a Feeling
When a car makes a hard left turn, passengers might feel "thrown" to the right of the car. Or at the bottom of a loop on a roller coaster, riders may feel pushed down into their seats.
These feelings are the result of inertia; however, not a force (though it may be referred to as an apparent force). Inertia describes the tendency of an object to resist changes in its motion, as described by Newton's First Law, the Law of Inertia.
When the car takes a sudden turn, or the roller coaster makes its plunge, the human bodies inside are already moving with some velocity in a particular direction. According to the Law of Inertia, these bodies initially resist changing their velocities.
The passengers are still moving forward in space when the car starts to go left abruptly - so rather than being "thrown right," the car is actually crashing into them from the left as it suddenly moves. Once their bodies catch up and start moving to the left as well, the crashing sensation ends.
Similarly in the roller coaster, the bodies are still moving downward when the coaster starts pushing upward on them. Until their bodies catch up to match the new velocity of the coaster, they feel like they are being thrown against the outside of the carts. Their bodies are still moving toward the carts as the carts now move toward their bodies.
How Centripetal Force Works
Centripetal force is only part of the recipe for making something move in a circle. The other ingredient is linear velocity. An object has to be moving when a centripetal force acts at a right angle to its motion in order for it to move in a circle.
Consider a ball on the end of a string. For a person to make it spin around their head, they have to first give it a toss with some horizontal component (in other words, not directly into or away from themselves). The person pulls the string taut, and the ball begins circling them rather than flying out.
Two things have to keep happening for the ball on the rope to keep spinning: The person must keep pulling the rope taut (by tugging it in), and they must keep adding slight horizontal nudges to maintain the ball's linear motion, which would otherwise slow down from friction with the air. (In space, however, the person would only need to pull the rope taught since the ball wouldn't lose any of its linear velocity while spinning in a vacuum.)
If the ball was not moving and the person pulled the rope taut, the ball would just move inward toward the person, not a circle. If the ball was moving directly out from the person, and they pulled on the rope, first the ball would slow down, then change direction and move back in towards the person, again not a circle.
In these cases, it wouldn't even make sense to call the force transmitted through the rope a centripetal force. It is simply an applied force of tension on the ball.
Sources of Centripetal Force
The word centripetal is just a way to describe any force acting perpendicular to an object's linear velocity. Many types of objects or interactions can provide centripetal forces.
For example, as already mentioned, a rope spinning in a circle provides centripetal force to an object tied on the end of it. A car turning around a bend experiences centripetal force from the friction between its tires and the road. A satellite in orbit continues moving in a circle due to the gravitational force providing a centripetal force toward the center of the Earth.
In each of these cases, if the source of the centripetal force were removed suddenly, the rope, the friction or gravity, the object would stop moving in a circle. More specifically, it would fly off at a tangent to that circle with whatever linear velocity it had.
Centripetal Force and Centripetal Acceleration
Because centripetal force is directed toward the center of an object's circular path and centrifugal force does not exist to counteract it, the object moving in a curved path must be experiencing a net force toward the center of the circle.
From Newton's Second Law, F = ma, it follows that a net force causes an acceleration. Indeed, anything moving in a circle has an acceleration, referred to as centripetal acceleration, toward the center of the circle.
This may seem counter-intuitive, considering that an acceleration means a changing velocity, yet plenty of things move in a circle at an apparently constant rate.
Here it helps to recall that velocity is a vector, with both a magnitude and a direction, and changing either of those results in a new velocity. As an object moves in a circle, both its linear velocity and centripetal acceleration are constantly changing direction; at any point along the path, the arrows for each vector will be facing a different way than at any other point along the path.
So the object continues traveling at the same speed but with a constantly changing direction. Physicists describe this as uniform circular motion.
How to Adjust Circular Motion
Because centripetal force is always perpendicular to an object's linear velocity, it describes the radius of the object's circular path. Therefore, the larger the centripetal force, the harder the "tug" inward, the tighter or smaller the circle will be, and the looser the centripetal force, the larger the circular path will be.
This might make sense intuitively: Pulling in on the rope holding the ball, or taking a curve on a sticky surface with more friction than on a slick one, like ice, will both result in smaller circular motions. Just remember that in any situation the only force causing the circular motion is an inward, centripetal force. No centrifugal force ever pushes an object "out" into a circle.