# Centrifugal Force

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## **CENTRIFUGAL FORCE ***an introduction* Edit

*an introduction*

**Definition- centrifugal force means "center fleeing" and is not a real force, but the perceived effect of inertia.**

As an object travels in a circle, it appears to have a force pulling it outward. This is called a **centrifugal force**. This force is not to be confused with a *centripetal force* which is the force *pulling* an object in to the center as it moves in a circle.

### CENTRIPETAL V. CENTRIFUGAL Edit

For every action there is an equal and opposite reaction. *Centripetal force*, an action, has the reaction of **centrifugal force**. The two forces are equal in magnitude and opposite in direction. Infact the newton's third law states every action is having equal and opposit reaction. However this cannot be indicated as "every force is having equal and opposite force" . There is a difference between force and action. The third law is true only for action and not for force alone.
**although the two forces have the same magnitude, they are significantly different**

- The centripetal force acts on the body in motion.

---> For example, if I were swinging a yo-yo in a circle, the centripetal force would be pulling in on the plastic part of the yo-yo

- The centrifugal force acts on the source of the centripetal force

--> For example, the centrifugal force would be pulling out on the person holding the string of the yo-yo

## **THE NONEXISTENT FORCE** Edit

Imagine you are in a car moving on a straight road. The road (and car) suddenly make a curve to the left and your body slams to the right. It feels as if there is a force pushing you to the right; however, there is none. Your body moves to the right because according to Newtons first law, an object moving in a straight line should not change direction unless a force is acted upon it. Your body naturally moves straight, the force is the car moving to the left.

It is the same situation with centrifugal force which is often refferred to as *The Nonexistent force*. For example, if you were to attach a ball to a string, hold the other end of the string and spin in a circle, it would feel as if the ball were pulling out on your arm. However, it is natural for the ball to go in a straight line (again, according to Newtons first law) so the centrifugal force that you feel is in fact just the nature of the ball working against the centripetal force that is pulling the ball into the circle.
Because we feel this "force" so strongly and regularly, we will treat it as if it was an actual force.

## A (VERY) BRIEF HISTORY Edit

There is only one name publicly known to be connected to the history of centrifugal force and that is Newton. Newton's laws of motion newton's 3 laws of motion have both shaped and initiated our understanding of centrifugal force, their concepts have been mentioned throughout this site.

## **THE MATHEMATICS** Edit

We can find the equation for centrifugal force by finding the equation for centripetal force because we know that the two forces are equal in magnitude.

We have already derived the formula for centripetal acceleration([[1]]) and know that ac=v^{2}/r or centripetal acceleration=velocity squared divided by the radius (in meters).
We also know that f=ma or force=mass times acceleration (for derivation click [[2]]).

When we combine these two equations we end up with

^{2}/r or

Now that we have the equation for centripetal force we almost have the equation for centrifugal force as well. The acceleration for centripetal force is aimed into the center of the circle but the acceleration for centrifugal force is aimed away from the circle. Therefor, because centripetal acceleration is positive and centrifugal acceleration is going in the oposite direction, it is negative.

### FINAL EQUATION FOR CENTRIFUGAL FORCEEdit

The final equation for centrifugal force is

^{2}/r

where...

f= force (in newtons)

m= mass (in kilograms)

v= velocity (in meters per second)

r= radius (in meters)

### TEST YOUR UNDERSTANDINGEdit

If the ball in the picture below has a mass of 2.5*10^{-2} kg, is moving at a rate of 3 m/s and has a centrifugal force of 4.5*10^{-1}, what is the radius of the string it is attached to?

- image taken from [3]

**SOLUTION**

The solution to this problem is: the radius equals 5*10^{-1} or .5 meters

we can find this solution by:
first solving the equation for "r" which leaves us with r=mv^{2}/Fc
we then plug in the values that we have which leaves us with r=(2.5*10^{-2}kg)(3^{2}m/s)/(4.5*10^{-1}N)
when we complete the calculations we get .5 meters

## USEFUL TERMS Edit

**centripetal acceleration**

In order for an object to execute circular motion - even at a constant speed - the object must be accelerating towards the center of rotation. This acceleration is called the centripetal or radial acceleration and has a magnitude of

ac = Centripetal acceleration SI: m/s2

vT = Tangential velocity or speed SI: m/s

r = Radius of object's path SI: m

w = Angular velocity SI: rad/s

this definition is from[4]

**centripetal force**

is the force that compels a body to move in a circular path. --

---> According to the law of inertia, in the absence of forces, an object moves in a straight line at a constant speed. An outside force must act on an object to make it move in a curved path. When you whirl a stone around on a string, you must pull on the string to keep the stone from flying off in a straight line. The force the string applies to the object is the centripetal force. The word centripetal is from two Latin words meaning to seek the center.

this definition is from [5]

**inertia**

Newton's first law of motion states that "An object at rest tends to stay at rest and an object in motion tends to stay in motion with the same speed and in the same direction unless acted upon by an unbalanced force." Objects "tend to keep on doing what they're doing." In fact, it is the natural tendency of objects to resist changes in their state of motion. This tendency to resist changes in their state of motion is described as inertia.

this definition is from [6]

## SOURCES Edit

http://www.aolsvc.worldbook.aol.com/wb/Article?id=ar103600&sc=-1

This site both quickly defines (if you only read the beginning)and goes into depth about centripetal force

http://www.ac.wwu.edu/~vawter/PhysicsNet/Topics/RotationalKinematics/CentripetalForce.html

Although you must have a background in physics to fully understand this site, it does a nice job of clearly defining centripetal and centrifugal forces as well as centripetal acceleration

http://csep10.phys.utk.edu/astr161/lect/history/newton3laws.html

This website describes Newton's three laws of motion with ease and clarity

http://www.glenbrook.k12.il.us/gbssci/phys/class/newtlaws/u2l1b.html

This site's definition of inertia is the one listed on my site, it also goes into further detail on the subject

http://www.infoplease.com/ce6/sci/A0811114.html

This site's description of the differences between centripetal and centrifugal forces is complicated and pretty hard to understand

http://observe.arc.nasa.gov/nasa/space/centrifugal/centrifugal6.html

This source provides a complex but extremely detailed derivation of the "final formula" for centrifugal force

http://phun.physics.virginia.edu/topics/centrifugal.html

This is a fun site that gives a very broad and simple difinition of centrifugal force

This site does a clear (yet somewhat sophisticated) job of describing the differences between centripetal and centrifugal forces

Zitzewitz, Paul W.,Ph.D. Physics: Principles and Problems. Colombus,OH: Glencoe/McGraw-Hill, 1999.

This textbook has only half a page on centrifugal force; however, it is worth reading and creates a clear picture of the subject