What is the difference between centripetal acceleration and centrifugal force?

Answer 1

Any object moving in a circle must have its velocity vector always changing direction (even if it is moving with a constant (instantaneous) speed). This acceleration is caused by the net force along the radius line of the circle the object is traveling on, and is called centripetal acceleration. The word centripetal refers to the fact (which we can demonstrate, if you like) that it always points from the object's position to the center of the circle, no matter where on the circle the object is.

The net force causing this acceleration, by the way, is called (not surprisingly, perhaps) the centripetal force. It is the actual net force acting on the object to keep it moving on the circle.

Imagine you are in a car traveling (with constant speed) around a circular path. Suppose the speed is fairly high and the curve pretty tight. You have a seatbelt on, but are not holding yourself particularly rigid. As you go through the curve, you find your head leaning the opposite way from the center of the curve.

You might describe this as your head being pulled by some force in a direction *away* from the center of the circle. However, the physics description is a little different. For you to go into the circle with the rest of the car, a centripetal force has to be applied to you.

For the car, the centripetal force comes from the static friction of the tires in contact with the road (imagine trying to take that curve on an icy road; the car would not turn, but go in a straight line off the road at the same speed, most likely, indicating insufficient centripetal force was applied to it). It is transmitted to every part of the car by the structural integrity of the vehicle.

For you, though, the centripetal force comes through your contact with the car, which mainly occurs on your feet, legs, and behind, up to the shoulder, if you are wearing a shoulder belt. That is where the centripetal force comes which pulls your body into the curve with the rest of the car.

But if you are not holding yourself rigid, your next can be pretty squishy. So your head does not "get the message" about going in the circle until a little after the rest of your body is already pulled in. It stays behind for a moment, with no centripetal force, trying to continue in the straight-line path it was on (as Newton's first law of motion says, an object will continue at constant velocity unless a net force acts on it). What finally pulls your head into the circle with the rest of you is tension exerted from the rest of your body through the neck, which does not happen until the rest of your body is already moving into the circle.

So physics says that what appears to be an outward force on your head ("centrifugal," or center-fleeing, force) is actually your head's inertial response to not having a centripetal force on it until just a bit after the rest of the body does. This is why "centrifugal" force is called a fictitious or apparent force. It is not really there, but it seems to be.

Imagine, though, we want to consider the car as a non-accelerating reference frame as it goes through the circle. In this case, we would ignore any idea of a centripetal force, and promote "centrifugal force" to the status of an actual force we have to deal with.

But when would we want to be so delusional as to ignore the fact we are going in a circle and act like we are in an non-accelerating (in other word, inertial) reference frame? We are usually very good about adjusting out understanding to the fact we are in motion. So when would be not be?

How about any time we want to consider ourselves at rest her on Earth? We are actually rotating at several hundred miles per hour (depending on latitude) around the Earth's axis. However, we do not usually work on a scale where we see the effect of that motion... UNTIL we start firing long-range ballistic shells. At this point, the fact of being on a rotating Earth becomes apparent, but it is usually easier to treat the shell as being subject to a centrifugal "force" to match up better with the idea that we are firing it "from rest."

If you have any further questions, please do not hesitate to ask.

Answer 2

Both speak of the same phenomenon, but the point of view is different. Centripetal acceleration is when you work in Galilean reference frame (or Inertial frame of reference). Centrifugal force is when you work with the rotating reference frame.

Answer 3

Centripetal force is the force required to accelerate an object in a circular path. It is F = ma, where a is the centripetal acceleration. a, in turn, is v² / r, where v is the tangential velocity.

Centrifugal force is often called an apparent force, and is associated with the inertia of the object. When an object is in a circular orbit with constant angular velocity, the centripetal and centrifugal forces are in balance.

https://en.wikipedia.org/wiki/Centripetal_force