Physics
Centrifugal Force
Centrifugal force is the apparent force that acts outward on a body moving around a center, arising from the body's inertia. It is a fictitious force that arises from the observer's frame of reference and is not a fundamental force of nature.
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12 Key excerpts on "Centrifugal Force"
eBook - ePub- Geoffrey K. Vallis(Author)
- 2011(Publication Date)
- Princeton University Press(Publisher)
If we understand these forces, we will be able to understand a great deal about the motion of the atmosphere and ocean, so let’s figure out what they are. We’ll begin with the forces that arise (or appear to arise) as a consequence of Earth’s rotation, namely Centrifugal Force and the Coriolis force, and then consider the pressure force. It turns out that for most geophysical applications, the Coriolis force is much more important than Centrifugal Force, but we need to understand the latter to understand the former, so that is where we begin. Centrifugal Force Suppose that you are riding in a train that starts to go around a bend rather quickly. You feel like you are being thrust outward toward the side of the car, and if you are really going quickly around a tight curve, you might have to hang onto something to stay put. The outward force that you are feeling is commonly known as Centrifugal Force. Strictly speaking, it is not a force at all (we’ll explain that cryptic comment later), but it certainly feels like one. What is going on? One of the most fundamental laws of physics, Newton’s first law, says that, unless acted upon by a force, a body will remain at rest or continue moving in a straight line at a constant speed. That is, to change either direction or speed, a body must be acted upon by a force. Thus, in order for you to go around a bend, a force must act (and act on the train too), and this force, whatever it may be in a particular situation, is called the centripetal force. Without that force, you would continue to go in a straight line. The Centrifugal Force that you feel is caused by your inertia giving you a tendency to try to go in a straight line when your environment is undergoing a circular motion, so you feel that you are being pushed outward. You do end up going around the bend because your seat pushes against you, providing a real force (the aforementioned centripetal force) that accelerates you around the bend
eBook - PDF- Raymond Serway, Chris Vuille(Authors)
- 2017(Publication Date)
- Cengage Learning EMEA(Publisher)
The magnitude of the of the net centripetal force equals the mass times the magnitude of the centripetal force equals the mass times the magnitude of the centripetal acceleration: F c c 5 ma c 5 m v 2 r [7.19] A net force causing a centripetal acceleration acts toward the center of the circu- lar path and effects a change in the direction of the velocity vector. If that force should vanish, the object would immediately leave its circular path and move along a straight line tangent to the circle at the point where the force vanished. Centrifugal (‘center-fleeing’) forces also exist, such as the force between two particles with the same sign charge (see Topic 15). The normal force that pre- vents an object from falling toward the center of the Earth is another example of Tip 7.2 Centripetal Force I s a Type of Force, N ot a Force in I tself! “Centripetal force” is a classifica- tion that includes forces acting toward a central point, like the horizontal component of the string tension on a tetherball or gravity on a satellite. A centripetal force must be supplied by some d by some d actual, physical force. Figure 7.9 A puck attached to a string of length r rotates in a horizontal plane r rotates in a horizontal plane r at constant speed. m r T ension T ension T T is the centripetal force keeping the puck on a circular path. S T S v S Copyright 2018 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. WCN 02-200-202 202 TOPIC 7 | Rotational Motion and Gravitation Unless otherwise noted, all content on this page is © Cengage Learning. APPLYING PHYSICS 7.2 ARTI F I C I AL G R AV ITY a Centrifugal Force. Sometimes an insufficient centripetal force is mistaken for the presence of a Centrifugal Force (see section 7.4.2 Fictitious Forces, page 206).
- David V. Guerra(Author)
- 2023(Publication Date)
- CRC Press(Publisher)
12 Circular Motion and Centripetal Force
DOI: 10.1201/9781003308065-1212.1 Introduction
Until this point in the volume, the motion of the objects studied has been predominantly in one dimension, so the change in the velocity of an object was focused on the change in the magnitude of the velocity vector. In this chapter, the change in velocity of an object in uniform circular motion is all about the change in the direction of the object’s velocity. Therefore, this motion, which is common in nature, requires its own analysis. First, by studying the change in the direction of the velocity vectors of an object moving in a circle at a constant speed the centripetal acceleration is derived. From the acceleration the associated net force, known as the centripetal force, is explained. Then, a series of examples employed in these concepts are provided in which the forces of tension, friction, gravity, electrostatics, and magnetism are involved.- Chapter question: A centrifuge is a device that separates solutions, like blood, into its different constituents by spinning the solution at high speeds. The solution is poured into test tubes, loaded into the centrifuge, and spun at a high rate until the constituents of the solution are separated. As a centrifuge spins faster, heavier particles in the solution move away from the center of the circle, toward the bottom of the test tube. In the case of blood, the denser red blood cells move to the outside of the circle with the largest radius r, as shown in Figure 12.1 , which is often referred to as the bottom of the tube, the white cells and platelets move to the center of the tube, and the blood plasma moves to the inside, which is the top of the tube.
FIGURE 12.1
eBook - PDF- Raymond Serway, Chris Vuille(Authors)
- 2017(Publication Date)
- Cengage Learning EMEA(Publisher)
The normal force that pre- vents an object from falling toward the center of the Earth is another example of Tip 7.2 Centripetal Force Is a Type of Force, Not a Force in Itself! “Centripetal force” is a classifica- tion that includes forces acting toward a central point, like the horizontal component of the string tension on a tetherball or gravity on a satellite. A centripetal force must be supplied by some actual, physical force. Figure 7.9 A puck attached to a string of length r rotates in a horizontal plane at constant speed. m r Tension T is the centripetal force keeping the puck on a circular path. S T S v S Copyright 2018 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. WCN 02-300 202 TOPIC 7 | Rotational Motion and Gravitation Unless otherwise noted, all content on this page is © Cengage Learning. APPLYING PHYSICS 7.2 ARTIFICIAL GRAVITY a Centrifugal Force. Sometimes an insufficient centripetal force is mistaken for the presence of a Centrifugal Force (see section 7.4.2 Fictitious Forces, page 206). A radial force is a vector and has a direction. The second law for uniform cir- cular motion involves forces that are directed either towards the center of a circle or away from it. A force acting towards the center of the circle is by convention negative. Examples include the gravity force on a satellite or the string tension of a whirling yo-yo. A force acting away from the center of the circle is positive. Exam- ples include the normal force on a car traveling over the circular crest of a hill or the force of repulsion between like electric charges. Similarly, the centripetal accel- eration is negative because it acts towards the center of the circle.
eBook - PDFApplied Engineering Technology NQF4 SB
TVET FIRST
- Sparrow Consulting(Author)
- 2013(Publication Date)
- Macmillan(Publisher)
They are: • rectilinear acceleration caused by the acceleration of the object in a straight line • Centrifugal Force caused by rotation • Coriolis force caused by rotation • Euler force caused by a variable rate of rotation, if and when that occurs. To explain the difference between an inertial and a non-inertial frame of reference, consider yourself in a car. When the car brakes or goes around a corner, you tend to move with the car, corresponding to the movements the car makes. You do not move because of an external force acting on you – you move because the car moves. This is an example of a non-inertial frame of reference. However, when someone pushes you from behind or bumps into you, you move because of the external force (friction) of the object acting on you. This is an inertial frame of reference. The Earth is the best example of a rotating frame of reference. The Earth is controlled by the Coriolis force and the Centrifugal Force. The Coriolis effect is the change in direction, speed or movement of a moving object because the object is present in a rotating frame of reference. The Coriolis effect does not appear when the motion is expressed in an inertial frame of reference. A Centrifugal Force is a force which is caused by rotation and moves away from the axis of rotation. It is therefore the reaction force to a centripetal force. A mass undergoing circular motion constantly accelerates toward the centre of the circle. This centripetal acceleration is caused by a centripetal force which is exerted on the mass by some other object. In accordance with Newton’s third law of motion, the mass exerts an equal and opposite force on the object. This is the real or reactive Centrifugal Force – it is directed away from the centre of rotation and is exerted by the rotating mass on the object which imposes the centripetal acceleration.
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Library Press(Publisher)
________________________ WORLD TECHNOLOGIES ________________________ Chapter- 4 History of Centrifugal and Centripetal Forces In physics, the history of centrifugal and centripetal forces illustrates a long and complex evolution of thought about the nature of forces, relativity, and the nature of physical laws. Huygens, Leibniz, Newton, and Hooke Early scientific ideas about Centrifugal Force were based upon intuitive perception, and circular motion was considered somehow more natural than straight line motion. According to Domenico Meli: For Huygens and Newton Centrifugal Force was the result of a curvilinear motion of a body; hence it was located in nature, in the object of investigation. According to a more recent formulation of classical mechanics, Centrifugal Force depends on the choice of how phenomena can be conveniently represented. Hence it is not located in nature, but is the result of a choice by the observer. In the first case a mathematical formulation mirrors Centrifugal Force; in the second it creates it. Christiaan Huygens coined the term Centrifugal Force in his 1659 De Vi Centrifiga and wrote of it in his 1673 Horologium Oscillatorium on pendulums. Isaac Newton coined the term centripetal force ( vis centripita ) in his discussions of gravity in his 1684 De Motu Corporum . Gottfried Leibniz as part of his solar vortex theory conceived of Centrifugal Force as a real outward force which is induced by the circulation of the body upon which the force acts. An inverse cube law Centrifugal Force appears in an equation representing planetary orbits, including non-circular ones, as Leibniz described in his 1689 Tentamen de motuum coelestium causis . Leibniz's equation is still used today to solve planetary orbital problems, although his solar vortex theory is no longer used as its basis. Leibniz produced an equation for planetary orbits in which the Centrifugal Force appeared as an outward inverse cube law force in the radial direction: .
No longer available |Learn morePhysics for Scientists and Engineers
Foundations and Connections, Extended Version with Modern Physics
- Debora Katz(Author)
- 2016(Publication Date)
- Cengage Learning EMEA(Publisher)
WCN 02-300 6-6 Centripetal Force 169 All content on this page is © Cengage Learning. If the origin of a polar coordinate system is at the center of the circle, the centripetal force is written as F u c 5 2m v 2 r r ˆ (6.8) The centripetal force is not a new force. It is not generated by the circular motion of a particle; instead, it is a requirement of circular motion. Some physical force (or forces)—gravity, a spring force, the normal force, a tension force, static friction— must act on an object in uniform circular motion in such a way that the net force on the object is perpendicular to the velocity and points to the center of the circular path. Neither drag nor moving friction can generate a centripetal force because they are always directed opposite the velocity. In the case of uniform circular motion, the net force is the centripetal force, which is always perpendicular to the velocity. So, imagine that the source of the centripetal force were suddenly removed such that there was no net force exerted on the object. Then, ac- cording to Newton’s first law, the object would continue at the same speed but in a straight line tangent to the point where the object was when the force suddenly vanished. CONCEPT EXERCISE 6.11 The following objects are moving in uniform circular motion. Draw a free-body dia- gram for each object and identify the force responsible for the centripetal acceleration. Object 1. A person riding on the barrel-of-fun ride (Fig. 6.27, top) Object 2. The lead object in the laboratory set-up (Fig. 6.27, center) Object 3. A jogger running on a circular track (Fig. 6.27, bottom) Barrel-of-fun rider Lead object attached to spring Runner on track FIGURE 6.27 Problems that involve centripetal force are no different from other problems that require us to apply Newton’s second law. So, the strategy developed in Section 5-8 works here.
eBook - PDFIntroduction to Fluid Dynamics
Understanding Fundamental Physics
- Young J. Moon(Author)
- 2022(Publication Date)
- Wiley(Publisher)
105 4 Curved Motions 4.1 Centrifugal Force Curved motion is a generic term but its implicated meaning goes beyond definition. The most fundamental physics of curved motion is the centrifugal effect, which is coupled with viscosity to make physics more complex and diverse. Curved motion is often associated with the flows of rotat- ing machineries (e.g. fans, compressors, and turbines) and vortex flows in nature (e.g. tornados, low-pressure cyclones, and fire whirl). It is also related to the complex dynamics of wall-bounded shear flows on curved walls (e.g. Coanda effect, origin of lift). 4.1.1 Radial Force Balance When a fluid undergoes curved motion, it is brought into a state of radial compression by two forces in action and reaction: the Centrifugal Force of the fluid (i.e. inertia force) versus the force exerted in the centripetal direction by reaction (Figure 4.1). The latter can be the reaction force from curved boundaries, or the fields under two different gravitational body forces (e.g. sink and surroundings). Therefore, the local pressure is determined by these two forces in action and reaction and also increases outward due to the mass accumulated in the radial direction. For a fluid in curved motion, the equation of motion can be set in the radial direction as follows: 𝜌 (dn dA) ⋅ a n = −dp n ⋅ dA (4.1) where dm = 𝜌 (dn dA), a n is the centripetal acceleration, dp n = (𝜕p∕𝜕n)dn is the pressure differ- ence in the radial direction, and n denotes the local coordinates normal (outward) to the streamline. The centripetal acceleration a n equals the product of the tangential flow speed v (= ds∕dt) and the rate of turn of the flow direction ̇ 𝜃 (= d𝜃∕dt) a n = −v ⋅ ̇ 𝜃 = −v ⋅ ds∕r c dt = − v 2 r c (4.2) where the negative sign indicates that the direction of action is in the centripetal direction, and r c is the local radius of curvature of the streamline.
eBook - ePubMid-Latitude Atmospheric Dynamics
A First Course
- Jonathan E. Martin(Author)
- 2013(Publication Date)
- Wiley(Publisher)
|). The direction of the ball changes continuously, however, and so, as viewed from the perspective of the ball, there is a uniform acceleration directed toward the axis of rotation equal to(2.15)This acceleration is called the centripetal acceleration and is caused by the force of the string pulling on the ball. Suppose you are on the ball and rotating with it. From your perspective the ball is stationary but, in reality, a centripetal acceleration is still being exerted upon it. In order for a person on the ball to apply Newton’s laws under this condition, an apparent force that exactly balances the true centripetal force must be included in the physics; this apparent force is known as the Centrifugal Force.Figure 2.5 The rotating ball on a string experiences an inward-directed centripetal acceleration, indicated by the dark arrow. To the observer on the ball, a compensating Centrifugal Force, indicated by the gray arrow, must be included to describe accurately motions on the ball itselfFigure 2.6 Relationship between the Centrifugal Force, gravitation (g *), and effective gravity (g ). The effect of the Centrifugal Force is to deform the Earth’s shape into an oblate spheroid on which the local vertical direction is perpendicular to effective gravity as shownIn order to balance the centripetal acceleration, the centrifugal acceleration is directed outward along the radius of rotation and is given by(2.16)As depicted in Figure 2.6 , on a rotating Earth, the Centrifugal Force affects the vertical force balance. When the Centrifugal Force and gravitational forces (g *) are added, the result is called effective gravity (g
eBook - PDFQuestioning the Universe
Concepts in Physics
- Ahren Sadoff(Author)
- 2008(Publication Date)
- Chapman and Hall/CRC(Publisher)
23 4 Forces 4.1 THE FUNDAMENTAL FORCES What is a force? One answer is that it is a push or a pull. A better answer, that we will find to be more useful, is that it is an interaction between two or more objects. For most of our discussion, two objects will suffice. Forces are no strangers to us since we interact with all sorts of things every day. Below is a list of forces I have compiled. Before reading my list, it would be instruc-tive for you to take out a piece of paper and make your own list. Hopefully you will come up with some not on my list. Gravity Electric Weak nuclear Strong nuclear Centrifugal Magnetic Centripetal Friction Wind force Contact force (between surfaces) Muscular force Chemical Atomic I am sure you have noticed that my list is arranged in columns or categories. Let us look at the last column first. Both items are, in fact, not forces at all, but adjec-tives describing the action of a particular force. A Centrifugal Force is any force that is directed outward from the center of a curve when an object is traveling in curved motion. Similarly, a centripetal force acts inward toward the center of the curve. Gravity is usually the force most people list first, as I have. It, of course, is very important to us since it keeps us bound to the earth and the earth to the sun. The second column contains many familiar forces under one heading. Why? Because all these seemingly different forces are all due to only one force. Electric and magnetic are not separate forces, but just different manifestations of what is known as the electromagnetic force (we will discuss this in more detail shortly). The force that holds the atom together is not some special new force, but is just due to the electri-cal attraction of the negatively charged electrons to the positively charged protons in the nucleus. Similarly, different atoms interact by the attraction or repulsion of the electrons and protons in one atom acting on the electrons and protons of another atom.
eBook - PDF- Paul Peter Urone, Roger Hinrichs(Authors)
- 2012(Publication Date)
- Openstax(Publisher)
It is a “center-seeking” force that always points toward the center of rotation. It is perpendicular to linear velocity v and has magnitude F c = ma c , which can also be expressed as F c = m v 2 r or F c = mrω 2 , ⎫ ⎭ ⎬ ⎪ ⎪ 6.4 Fictitious Forces and Non-inertial Frames: The Coriolis Force • Rotating and accelerated frames of reference are non-inertial. • Fictitious forces, such as the Coriolis force, are needed to explain motion in such frames. 6.5 Newton’s Universal Law of Gravitation • Newton’s universal law of gravitation: Every particle in the universe attracts every other particle with a force along a line joining them. The force is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. In equation form, this is 228 Chapter 6 | Uniform Circular Motion and Gravitation This OpenStax book is available for free at http://cnx.org/content/col11406/1.9 F = G mM r 2 , where F is the magnitude of the gravitational force. G is the gravitational constant, given by G = 6.674×10 –11 N ⋅ m 2 /kg 2 . • Newton’s law of gravitation applies universally. 6.6 Satellites and Kepler’s Laws: An Argument for Simplicity • Kepler’s laws are stated for a small mass m orbiting a larger mass M in near-isolation. Kepler’s laws of planetary motion are then as follows: Kepler’s first law The orbit of each planet about the Sun is an ellipse with the Sun at one focus. Kepler’s second law Each planet moves so that an imaginary line drawn from the Sun to the planet sweeps out equal areas in equal times. Kepler’s third law The ratio of the squares of the periods of any two planets about the Sun is equal to the ratio of the cubes of their average distances from the Sun: T 1 2 T 2 2 = r 1 3 r 2 3 , where T is the period (time for one orbit) and r is the average radius of the orbit. • The period and radius of a satellite’s orbit about a larger body M are related by T 2 = 4π 2 GM r 3 or r 3 T 2 = G 4π 2 M.
Available until 25 Jan |Learn more- Tai L. Chow(Author)
- 2013(Publication Date)
- CRC Press(Publisher)
155 © 2010 Taylor & Francis Group, LLC Motion Under a Central Force A central force is a force whose line of action passes through a single point or center (fixed or in motion with constant velocity) and whose magnitude depends only on the distance from the center. Forces, such as gravity and electrostatic force, are all central forces. Perhaps the first example of central force motion to be recognized was that of the planets about the sun. In old quantum theory, Bohr’s hydrogen atom was described in terms of a classical two-body central picture. Certain two-body nuclear interactions, such as the scattering of alpha particles by nuclei, undoubtedly have a central character. 6.1 TWO-BODY PROBLEM AND REDUCED MASS Consider a conservative system of two particles of mass m 1 and m 2 . We shall limit ourselves to the case where the only forces acting are equal and opposite, directed along the line connecting the masses. Such a system has six degrees of freedom and, hence, six independent generalized coordinates. We can select these to be the three components of arrowrightnosp r 1 and the three components of arrowrightnosp r 2 . Alternatively, we can choose the three components of the position vector arrowrightnosp R of the center of mass (CM) of the system and the three components of arrowrightnosp arrowrightnosp arrowrightnosp r r r ( ) = -1 2 . Components arrowrightnosp ′ r 1 and arrowrightnosp ′ r 2 are position vec-tors of m 1 and m 2 with respect to the CM. The relationships among the various position vectors are illustrated in Figure 6.1. The position vector arrowrightnosp R of the center mass is given by arrowrightnosp arrowrightnosp R m r m r m m = + + 1 1 2 2 1 2 (6.1) and so in the CM system, m r m r 1 1 2 2 0 arrowrightnosp arrowrightnosp ′+ ′ = from which we have arrowrightnosp arrowrightnosp ′ = -′ r m m r 2 1 2 1 ( ) / .
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