# Centripetal and Centrifugal force

• kghosh
In summary, the conversation discusses the concept of centrifugal force and how it is not actually a true force, but rather a mathematical concept used for convenience. The conversation also touches on the difference between interaction forces and inertial forces, and how they are related to the concept of centripetal force. It is noted that the force that the yo-yo exerts on the finger along the string is simply a reaction force.

#### kghosh

I just read that Centrifugal Force is a false force. It does not exist. Inertia (which is not a force) is mistakenly called Centrifugal force. Now, here is my question

According to Newton's 3rd law of motion, forces always exist in pairs; action and reaction. Centripetal force which is the force acting on the body pushing it towards the center must have a pair that is the force acting on the object that is exerting the centripetal force. For example: a yo-yo twirled around a finger is pulled along the string by the finger towards the finger - centripetal force. The force with which the yo-yo pulls on the finger along the string What is that force called then? This has nothing to do with the inertia of the yo-yo which will make it fly along a straight line as soon as the centripetal force is moved.

kghosh said:
I just read that Centrifugal Force is a false force. It does not exist.
It is an inertial force, not an interaction force. In a rotating frame it "exists" in the same sense as interaction forces do:
http://en.wikipedia.org/wiki/Centrifugal_force_(rotating_reference_frame)
kghosh said:
Inertia (which is not a force) is mistakenly called Centrifugal force.
It is not a "mistake" but a practical mathematical concept:
http://en.wikipedia.org/wiki/Fictitious_force

kghosh said:
According to Newton's 3rd law of motion, forces always exist in pairs; action and reaction.
Note that this law applies only to interaction forces, not inertial forces. But you are correct that the interaction centripetal force must have a equal but opposite force, according to Newtons 3rd.

kghosh said:
Centripetal force which is the force acting on the body pushing it towards the center must have a pair that is the force acting on the object that is exerting the centripetal force. For example: a yo-yo twirled around a finger is pulled along the string by the finger towards the finger - centripetal force. The force with which the yo-yo pulls on the finger along the string What is that force called then?
Some call it "reactive centrifugal force":
http://en.wikipedia.org/wiki/Reactive_centrifugal_force

Note that contrary to the "inertial centrifugal force" in a rotating ref. frame this "reactive centrifugal force" is an interaction force that exists in all ref. frames. See the table in this section for a comparison of the two:
http://en.wikipedia.org/wiki/Reactive_centrifugal_force#Relation_to_inertial_centrifugal_force

Here another example to explain all three forces, a rotating space station with two astronauts:

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hi kghosh!
kghosh said:
I just read that Centrifugal Force is a false force. It does not exist. Inertia (which is not a force) is mistakenly called Centrifugal force.

there is no centrifugal force for an inertial observer

there is centrifugal force for an observer in a rotating frame

centrifugal force is a fictititious (or inertial) force … some observers create it for their convenience
a yo-yo twirled around a finger is pulled along the string by the finger towards the finger - centripetal force. The force with which the yo-yo pulls on the finger along the string What is that force called then?

just a reaction force

## 1. What is the difference between centripetal and centrifugal force?

Centripetal force refers to the inward force that keeps an object moving in a circular path. It is directed towards the center of the circular motion. On the other hand, centrifugal force is an outward force that appears to act on a body moving in a circular path, pulling the body away from the center of the circle. It is a fictitious force that arises due to the inertia of the object.

## 2. What are some real-life examples of centripetal and centrifugal force?

Centripetal force can be observed in the motion of a satellite orbiting around the Earth, the rotation of a ball tied to a string, or a car turning on a curved road. Centrifugal force can be seen in the spinning of a washing machine, the motion of a rollercoaster, or the movement of a child on a merry-go-round.

## 3. How are centripetal and centrifugal force related to each other?

Centripetal and centrifugal force are two sides of the same coin. Centripetal force is responsible for keeping an object moving in a circular path, while centrifugal force is the result of the object's tendency to resist this inward force. These two forces are equal in magnitude and opposite in direction, and together they maintain the object's circular motion.

## 4. Can centripetal and centrifugal force be calculated?

Yes, both centripetal and centrifugal force can be calculated using the same formula: F = m*v^2/r, where F is the force, m is the mass of the object, v is the velocity, and r is the radius of the circular motion. The only difference is that for centripetal force, the value of r is positive, while for centrifugal force, it is negative.

## 5. Are centripetal and centrifugal force the only forces acting on an object in circular motion?

No, there are other forces that may act on an object in circular motion, such as friction and air resistance. However, centripetal and centrifugal force are the only forces that are directly responsible for maintaining the object's circular motion. The other forces may affect the object's speed or direction, but they do not play a role in keeping the object in a circular path.