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## PowerPedia:Centrifugal force

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Centrifugal force is a term which may refer to two different Forces which are related to There was an error working with the wiki: Code[6]. Both of them are oriented away from the There was an error working with the wiki: Code[7], but the object on which they are exerted differs. The Latin word centrum of which the term is derived stands for "center" and teh ending fugere means "to flee". Generally, a centrifugal force is a Force that pushes in a direction that is away from the center of a circular path.

#### Introduction

The physical reaction of centrifugal forces result in a reaction of Centripetal force This is equal in magnitude to the centripetal force, directed away from the center of rotation, and is exerted by the rotating object upon the object which exerts the centripetal force. As it is an actual force, it is always present, independent of the choice of [[reference frame]. Note that the Newtonian use of the term centrifugal force is rare in mainstream physics discussions. A rotating reference frame fictitious centrifugal force appears when a rotating reference frame is used for analyzing the system. The force does not arise from any physical interaction, but rather from the acceleration a of the non-inertial reference frame itself. The apparent centrifugal force is exerted on all objects, and directed away from the axis of rotation. Both of these can be observed in action on a passenger riding in a car. If the car swerves around a corner, the passenger's body pushes against the outer edge of the car. This is the reactive centrifugal force, which is called a reaction force because it results from passive interaction with the car which actively pushes against the body. Using a reference frame which is fixed relative to the car (a model which those inside the car will often find natural) and while ignoring its rotation, it looks like an external force is pulling the passenger out of the car. This is the fictitious centrifugal force, so called because it is not an actual force exerted by some other object.

#### Assumed centrifugal forces

Dealing with a rotating frame of reference with Newton's laws of motion artificially valid, one can add fictitious forces that are assumed to be the cause of acceleration. In particular, the centrifugal acceleration is added to the motion of every object, and attributed to a fictitious centrifugal force, given by:

:{F}_{centrifugal} = m \omega^2 {r}_\perp \,

: or

:{F}_{centrifugal} = m {a}_{centrifugal} \,

where m\, is the mass of the object. This centrifugal force is a sufficient correction to Newton's second law only if the body is stationary in the rotating frame. For bodies that move with respect to the rotating frame it must be supplemented with a fictitious There was an error working with the wiki: Code[8]. For example, a body that is stationary relative to the non-rotating frame, will be rotating when viewed from the rotating frame. The centripetal force of -m \omega^2 {r}_\perp required to account for this apparent rotation is the sum of the centrifugal force (m \omega^2 {r}_\perp) and the Coriolis force

(-2m {\omega \times v} = -2m \omega^2 {r}_\perp). Since this centripetal force includes contributions from only fictitious forces, it has no reactive counterpart.

The assumed centrifugal force can be described by a Potential energy of the form E_p = -\frac{1}{2} m \omega^2 r_\perp^2. Such potential energy of the centrifugal force is often used in the calculation of the height of the There was an error working with the wiki: Code[9]s on the Earth (where the centrifugal force is included to account for the rotation of the Earth around the Earth-Moon center of mass). The principle of operation of the There was an error working with the wiki: Code[10] also can be simply understood in terms of this expression for the potential energy, which shows that it is favorable energetically when the volume far from the axis of rotation is occupied by the heavier substance.

#### Reactive force

When viewed from an There was an error working with the wiki: Code[11], the application of There was an error working with the wiki: Code[12] is simple. The a subject's inertia resists There was an error working with the wiki: Code[13], keeping the subject moving with constant speed and direction travel as the turn begins. From this point of view, the subject does not gravitate toward the outside instead, the curves meet the subject.

The force is then applied in a sidewise fashioon to accelerate the subject around a turn. This force is called a centripetal ("center seeking") force because its vector changes direction to continue to point toward the center of the car's arc as the car traverses it.

Being opposite, a reaction force is directed away from the center, therefore centrifugal. It is critical to realize that this centrifugal force acts upon the car, not the passenger.

The centrifugal reaction force with which the passenger pushes back against the door of the car is given by,

:{F}_{centrifugal} = - m {a}_{centripetal} \,

and then,

:{F}_{centrifugal} = m \omega^2 {r}_\perp \,

where m\, is the mass of the rotating object.

#### Rotating reference frames

In the classical approach, the inertial frame remains the true reference for the laws of mechanics. When using a There was an error working with the wiki: Code[14], the laws of physics are mapped from the most convenient inertial frame to that rotating frame. Assuming a constant rotation speed, this is achieved by adding to every object two coordinate accelerations which correct for the rotation of the coordinate axes, {a}_{rot} = {a} - 2{\omega \times v} - {\omega \times (\omega \times r)} \,,

and then {a}_{rot} ={a + a_{Coriolis} + a_{centrifugal}} \,, where {a}_{rot}\, is the acceleration relative to the rotating frame, {a}\, is the acceleration relative to the inertial frame, {\omega}\, is the There was an error working with the wiki: Code[15] vector describing the rotation of the reference frame, {v}\, is the velocity of the body relative to the rotating frame, and {r}\, is a vector from an arbitrary point on the rotation axis to the body. A derivation can be found in the article There was an error working with the wiki: Code[16]. The last term is the centrifugal acceleration, so the equation is {a}_{centrifugal} = - {\omega \times (\omega \times r)} = \omega^2 {r}_\perp

where {r_\perp} is the component of {r}\, perpendicular to the axis of rotation.

If there are two frames, one inertial and one rotating with a constant angular velocity \vec \omega, a time derivative of a vector in the rotating frame, \left ( \frac{d}{dt} \right ) _r, can be transformed to the time derivative in the inertial frame. Acceleration is a second derivative of position with respect to time. After applying the transformation to the position vector \vec r , the rotating reference frame is rotating constantly in the same direction - \vec \omega is a contant vector - and its time derivative is zero. Putting in \vec a for \left ( \frac{d^2 \vec r}{dt^2} \right ) and \vec v_r for \left ( \frac{d \vec r}{dt} \right ) _r, the equation is \vec a_i = \vec a_r + 2 \vec \omega \times \vec v_r + \vec \omega \times \left ( \vec \omega \times \vec r \right ). Moving things to the other side, but reversing one cross-product in each term, you find \vec a_r = \vec a_i + 2 \vec v_r \times \vec \omega + \vec \omega \times \left ( \vec r \times \vec \omega \right ). This tells us that \vec a_r, the acceleration of some object at \vec r as observed by someone at rest in the rotating frame is equal to the acceleration, \vec a_i, as observed by an observer in the inertial, non-rotating frame, plus 2 \vec v_r \times \vec \omega, which is the There was an error working with the wiki: Code[17]'s contribution to the acceleration, and \vec \omega \times \left ( \vec r \times \vec \omega \right ), which is the There was an error working with the wiki: Code[18] term.

#### Centrifugal statics

Consider a object that swings around a stationary pivot to which it is There was an error working with the wiki: Code[19]ed by a light, strong anchor line. There is tension in the anchor line, pulling inwards on the object (the centripetal force) and simultaneously pulling outwards on the pivot (the reactive centrifugal force). The tension is real, so these two forces still exist if we move to a corotating frame. However, in the rotating frame there is also a fictitious centrifugal force that pulls outwards on the object . It is distinct from the reactive centrifugal force that pulls outward on the pivot. When solving There was an error working with the wiki: Code[20] problems in a rotating frame (e.g. when calculating the internal stresses in a Flywheel) it is convenient to think of the fictitious centrifugal force as being transmitted through the tether line and becoming the pull on the pivot. In statics one often considers a force "the same" before and after it has been conveyed by a structural element, so according to this view the reaction force on the pivot is the fictitious force.

This identification as such by many in the mainstream often leads to confusion about the "fictitious" nature of the centrifugal force, because the pull on the pivot is a perfectly real force. The confusion can be resolved by noting that the distinction between fictitious and real forces depends on the frame of reference that one chooses. On the other hand, considering the reaction force to be the fictitious force is only valid in There was an error working with the wiki: Code[21], that is, once it is decided to always use a particular reference frame in which the entire system is stationary. The convenience of viewing a transmitted force as the same as the original force comes at the cost of a meaningful distinction between whether a force is real or fictitious.

#### Confusion and misconceptions

Centrifugal force can be a confusing term because it is misused (or used) in more than one instance, and because certian professional labeling can obscure which forces are acting upon which objects in a system (which is true for physics in general). When diagramming forces in a system, one must describe each object separately, attaching only those forces acting upon it (not forces that it exerts upon other objects). One can avoid dealing with fictitious forces entirely by analyzing systems using inertial frames of reference and when convenient, one simply maps to a rotating frame without forgetting about the frame rotation. Such is standard practice in mechanics textbooks.

Because rotating frames are not vital for understanding mechanics, many in the mainstream often de-emphasize the fictitious centrifugal force that appears to exist in a rotating reference frame. However, in the usual zeal of the mainstream to stamp out alternative understandings of the term in this case, they have sought to expunge it from the language entirely. Most hear of this force and equate centrifugal force to experiences that they have had in their lives. Most have been in a vehicle that has taken a turn and will recognize that there was a force acting on them, which caused them to move away from the turn.

##### Examples

Question:A standing passenger is riding on the bus as the bus takes a left hand turn. What happens to the passenger?

Misconception:The passenger is flung to the right of the bus because of a centrifugal force.

Explanation:There is no force acting on the passenger. The passenger is moving in the same direction while the bus turns. Since the bus is moving out from under the passenger, the passenger ends up on the right side until the wall of the bus stops him or her. Only then is there a force on the passenger from the wall.

Question:A man is riding on a circular amusement ride where he has his back on the wall and the floor is dropped. The rider does not move down on the wall. What directions are the net forces are on the rider?

Misconception:The force on the rider is towards the outside of the circle as well as a gravitational force down. The rider does not fall because he is being pushed against the wall.

Explanation:The force on the rider is towards the center of the circle. This force is from the wall keeping the rider in his circular path. If the wall were to disappear, the rider would continue in a straight-line tangent to the circle. The rider does not fall because the force due to friction and gravity are equal in magnitude and opposite in direction.

##### Overcoming Misconceptions

Many in the mainstream sciences have applied several different approaches to eliminate the mmore general conception. Savage and Williams (1989) gave several suggestions to help avoid the precieved problem. First they suggested that force diagrams should not include any non-Newtonian forces (those forces caused by another body). This will help alleviate any problems with phantom forces. They also suggested an approach to teaching circular motion without mentioning the term "centrifugal force," though they admit the need to mention it if the preconceived notion exists. Another study showed that only 19% of those could correctly identify the direction of forces on a person riding a circular amusement ride. However, Angell (2004) realized the need to address the There was an error working with the wiki: Code[22] that those have in order to overcome them with the proper scientific explanations. Most intuitive ideas do not need to be replaced but rather refined because there is something correct in most incorrect thought. A strategy given in a third article to help overcome this preceived misconceptions is providing a history of the concept being taught (Stinner 2001). Specifically, this article tells of the struggles that Newton had when he was trying to come up with his laws for circular motion. Newton’s predecessors were convinced of the same misconception that most those today. They believed that when dealing with rotational motion, there was a centrifugal force outward instead of a centripetal force inward. While teaching the history of the concept, the those learn why their misconceptions (assuming they exist) do not work, and those that did not have misconceptions are given a better understanding of how those concepts came to fruition.

#### Applications

A There was an error working with the wiki: Code[23] regulates the speed of an engine by using spinning masses that respond to centrifugal force generated by the engine. If the engine increases in speed, the masses move and trigger a cut in the There was an error working with the wiki: Code[24].

Centrifugal forces can be used to generate Artificial gravity. Proposals have been made to have gravity generated in space stations designed to rotate. The There was an error working with the wiki: Code[25] will use study the effects of There was an error working with the wiki: Code[26] level gravity on mice with simulated gravity from centrifugal force.

There was an error working with the wiki: Code[27]s are used in science and industry to separate substances by their relative masses.

Some There was an error working with the wiki: Code[5]s makes use of centrifugal forces. For instance, a There was an error working with the wiki: Code[28]’s spin forces riders against a wall and allows riders to be elevated above the machine’s floor in defiance of Earth’s gravity.

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Sources

John baez, So-called, sci.physics May 2 1997.

Centrifugal Force, hyperphysics.phy-astr.gsu.edu

gravitee, Newton's description in Principia, tripod.com.

Centrifugal force, Columbia electronic encyclopedia (nfoplease.com)

Centrifugal force, observe.arc.nasa.gov, TRW Inc., 1999.

Centrifugal Force scienceworld.wolfram.com, (There was an error working with the wiki: Code[29])

Centrifugal and Coriolis forces, sos.bangor.ac.uk (Java applet)

M. Alonso and E.J. Finn, Fundamental university physics, Addison-Wesley

Centripetal force vs. Centrifugal force - from an online Regents Exam physics tutorial by the Oswego City School District

Angell, Carl. Exploring students' intuitive ideas based on physics items in TIMSS. 1995. The 1st IEA International Research Conference. University of Oslo. 2004

Savage, M. D. and Williams, J. S. Centrifugal force: fact or fiction?. Physics Education. May 1989 Volume: 24 Start Page: 133

Stinner, Arthur. Linking ‘The Book of Nature’ and ‘The Book of Science’: Using Circular Motion as an Exemplar beyond the Textbook. Science & Education. Volume 10, Issue 4, Jul 2001. Pages 323 – 344

Mendelson, Alexander, Effect of centrifugal force on critical flutter speed on a uniform cantilever beam, NACA RM-E8B05, June 18, 1948.

There was an error working with the wiki: Code[1], Wikipedia: The Free Encyclopedia. Wikimedia Foundation.