# Fermilab

## Inquiring Minds

Centripetal or Centrifugal Force?

You Wrote:
A recent debate ended in a total draw. It was concverning centrifugal force, or its lack there of. Both sides of the argument stand for and against this common rule of physics. Centripital force was the only force affecting rotating objects, one litigator announced. My question for you is, is there such a thing as centrifugal force, or has it proven to be non-existent?

Thank You very much
A mediating Scientist

Hi,

thanks for your question, you are right, it is a little bit tricky to figure out what forces caused a given motion. In my explanation I assume you know what inertial and non inertial systems are. ( Inertial=moving with a constant speed [including speed=0], non-inertial=moving with acceleration.) They will play a very important role to distinguish between the centripetal and centrifugal forces. ( As you see, now I already told you, yes there are both forces existing in physics.)

1) Let us sit in an INERTIAL system. Suppose we have two small balls ( small to exclude their gravitational interaction). The first one (ball A) is at rest, at the origin, and the second one (ball B) is moving with a CONSTANT SPEED in an arbitrary direction. (But NOT towards the center of the ball A.) Since B moves with a constant speed, Newton's law says there is no force acting on B, therefore it moves on a straight line.

1a) Imagine, that we charge A with a positive charge, and B with a negative charge. The situation now dramatically changes, since there is a force acting on B by A. This force is the electric force, and the direction of the force is towards the center of A. We say, the force has a centripetal direction. THERE ARE NO OTHER FORCES ACTING ON B! (Note, I did not say anything about forces acting on A yet. Ball A just sits in the origin, being tightly glued there.) According to Newton's laws ( and also according to your everyday experience), ball B starts to ROTATE around the ball A and will do so, until the electric force acts. That simple it is.

2a) The above mind experiment can be applied to other situations. I will mention a few. In parentheses I indicate the correspondence with 1a.

• a ball ( B) on the end of a rope (electric force) rotating around your hand (A)
• the moon ( B) rotating around the Earth ( A). The rotation is caused by the gravitational force (electric force)
• a roller-coaster car ( B) in the circular loop ( A), where the centripetal force is the force acting by the loop on the car,
• a school bus (B) on an intersection turning left. The road is the analogy of the ball A and the friction force between the road and the tires is the analogy of the electric force.
• many more examples, where you have objects in a circular motion.
Now we understand, that the centripetal force acting on B causes its circular motion. But where is the centrifugal force??? What is it? The third Newton's law says: If A acts on B by a force, B acts on A by another force, called the reaction force, which has the same magnitude but opposite direction. Many people confuse the centrifugal force with this reaction force acting ON A BY B. ( As an illustration of the reaction force, just remember, that if you rotate a ball (B) on the end of a rope, your hand ( A) FEELS a force, which is the reaction force to the centripetal force.) Please remember, this reaction force is not the centrifugal force introduced by physicist. The reacting force does not act on B. Let us uncover this mystery now.

2) To explain the notion of the centrifugal force, I proceed similarly as in 1) but let us have now the ball B traveling in a school bus which initially moves with a constant speed. Let us have the ball B sitting at rest on the floor of the bus. Let us see, what we observe from the bus' frame of reference. Initially the bus was an inertial system, but when the bus turns left, it becomes a NON-INERTIAL system ( because it accelerates). An observer in the bus sees the ball B initially sitting at rest, but all over the sudden (when the bus starts to turn), the ball starts to roll. So the observer MUST CONCLUDE, that there IS a force acting on the ball. If he watches carefully, he sees that the ball moved in the radial direction ( away from the center of the curve). The observer calls this force the centrifugal force. However, as you probably figured, this force is not a real force, the ball moves due to the Newton's first law of inertia. It keeps moving straight with respect to any INERTIAL SYSTEM as it did before the bus started to turn. The centrifugal force arose exclusively due to the description of the ball by using a "wrong", NON-INERTIAL system of reference. Of course, when the ball hits the bus wall, its motion will start to be accelerated by the centripetal force by which the wall acts on the ball. It will turn with the bus.

A very interesting phenomena is related to the above. On the northern hemisphere due to the Earth rotation a bullet from a gun tends to decline to the right. (With respect to the direction it was shot.) The force which does this is called the Coriolis force, but that is a subject for another story.

- bye,
Arnold Pompos

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