Physics
Centripetal and Centrifugal Force
Centripetal force is the inward force that keeps an object moving in a circular path, directed towards the center of the circle. Centrifugal force is the apparent outward force experienced by an object moving in a circular path, which is actually a result of the object's inertia. These forces are important in understanding circular motion and are key concepts in physics.
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10 Key excerpts on "Centripetal and 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).
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: .
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.
- 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
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 - 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.
- Raymond Serway, John Jewett(Authors)
- 2018(Publication Date)
- Cengage Learning EMEA(Publisher)
(b) Overhead view observed by someone in an inertial reference frame attached to the platform. The platform appears stationary, and the ground rotates counterclockwise. PITFALL PREVENTION 6.2 Centrifugal Force The commonly heard phrase “centrifugal force” is described as a force pulling outward on an object moving in a circular path. If you are feeling a “centrifugal force” on a rotating carnival ride, what is the other object with which you are interact- ing? You cannot identify another object because it is a fictitious force that occurs when you are in a noninertial reference frame. Example 6.7 Fictitious Forces in Circular Motion Consider the experiment described in the opening storyline: you are riding on the Mad Tea Party ride and holding your smartphone hanging from a string. Now suppose your friend stands on solid ground beside the ride watching you. You hold the upper end of the string above a point near the outer rim of the spinning tea cup. Both the inertial observer (your friend) and the noninertial observer (you) agree that the string makes an angle u with respect to the vertical. You claim that a force, which we know to be fictitious, causes the observed deviation of the string from the vertical. How is the magni- tude of this force related to the smartphone’s centripetal acceleration measured by the inertial observer? S O L U T I O N Conceptualize Place yourself in the role of each of the two observers. The inertial observer on the ground knows that the smartphone has a centripetal acceleration and that the deviation of the string is related to this acceleration. As the noninertial observer on the teacup, imagine that you ignore any effects of the spinning of the teacup, so you have no knowledge of any centripetal acceleration. Because you are unaware of this acceleration, you claim that a force is pushing sideways on the smart- phone to cause the deviation of the string from the vertical.
eBook - PDF- Paul Peter Urone, Roger Hinrichs(Authors)
- 2012(Publication Date)
- Openstax(Publisher)
This geocentric model, which can be made progressively more accurate by adding more circles, is purely descriptive, containing no hints as to what are the causes of these motions. (b) The Copernican model has the Sun at the center of the solar system. It is fully explained by a small number of laws of physics, including Newton’s universal law of gravitation. Glossary ω , the rate of change of the angle with which an object moves on a circular path Δs , the distance traveled by an object along a circular path the curve in a road that is sloping in a manner that helps a vehicle negotiate the curve the point where the entire mass of an object can be thought to be concentrated a fictitious force that tends to throw an object off when the object is rotating in a non-inertial frame of reference the acceleration of an object moving in a circle, directed toward the center any net force causing uniform circular motion the fictitious force causing the apparent deflection of moving objects when viewed in a rotating frame of reference a force having no physical origin a proportionality factor used in the equation for Newton’s universal law of gravitation; it is a universal constant—that is, it is thought to be the same everywhere in the universe the angle at which a car can turn safely on a steep curve, which is in proportion to the ideal speed the sloping of a curve in a road, where the angle of the slope allows the vehicle to negotiate the curve at a certain speed without the aid of friction between the tires and the road; the net external force on the vehicle equals the horizontal centripetal force in the absence of friction the maximum safe speed at which a vehicle can turn on a curve without the aid of friction between the tire and the road an environment in which the apparent net acceleration of a body is small compared with that produced by Earth at its surface 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 an accelerated frame of reference Chapter 6 | Uniform Circular Motion and Gravitation 227
- Paul Anthony Russell(Author)
- 2021(Publication Date)
- Reeds(Publisher)
However, the forces set up by the vibration caused by out-of-balance weights far exceed the additional energy required to rotate the additional balancing weight. A B C D r r 1 r 2 r 3 m 3 m 2 a b c d m 1 m m 2 r 2 m 1 r 1 m 3 r 3 mr ▲ Figure 5.8 Space and vector diagrams for several coplanar forces Centripetal Forces • 113 Example 5.9. Two masses are fixed at right angles to each other on a disc which is to rotate; one is 3 kg at a radius of 125 mm from the centre of rotation, and the other is 4 kg at 150 mm radius. Find the position to fix a balance mass of 7 kg to equalize the centrifugal forces. Vector ab is drawn to represent force AB, represented by 3 × 0.125 = 0.375. Vector bc is drawn to represent force BC, represented by 4 × 0.15 = 0.6. ac r r = + × = = = = = 0 375 0 6 7 0 7075 0 101 101 0 375 0 6 0 625 2 2 . . . . tan . . . m mm α α = ° = ° + ° = ° 32 32 90 122 θ Therefore, the 7 kg counterbalance should be placed at a radius of 101 mm, at 122º to the 3 kg mass. Again, note carefully that the actual forces are centrifugal forces, each of value mω 2 r, but since all rotate at the same angular velocity, each force can be represented by m × r. Stress in Flywheel Rims due to Centrifugal Force Stress is the load or force carried by a material per unit of cross-section (see Chapter 9). stress total load area of cross-section = a b c 0.6 0.375 A B C r 7 kg 4 kg 0.125 m 0.15 m 3 kg 7 × r α θ ▲ Figure 5.9 3 and 4 kg masses rotating at right angles to each other 114 • Applied Mechanics Referring to Figure 5.10, considering the equilibrium of a small piece of the flywheel rim, it can be seen from the vector diagram of forces that the outward radial centrifugal force is balanced by the circumferential tensile force in the rim. This tension tends to snap the material; the stress, expressed by dividing the total tensile force by the area, is therefore termed the tensile stress or hoop stress.
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