Physics
Centripetal Force and Velocity
Centripetal force is the inward force that keeps an object moving in a circular path. It is always directed towards the center of the circle. The velocity of an object moving in a circular path is constantly changing in direction, but its speed remains constant due to the centripetal force.
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11 Key excerpts on "Centripetal Force and Velocity"
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 - PDF- John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler, Heath Jones, Matthew Collins, John Daicopoulos, Boris Blankleider(Authors)
- 2020(Publication Date)
- Wiley(Publisher)
And most drivers know that such turns ‘feel’ different. This feeling is associated with the force that is present in uniform circular motion, and we turn to this topic in the next section. CHAPTER 5 Dynamics of uniform circular motion 123 5.3 Centripetal force LEARNING OBJECTIVE 5.3 Solve uniform circular motion dynamic problems. Newton’s second law indicates that whenever an object accelerates, there must be a net force to create the acceleration. Thus, in uniform circular motion there must be a net force to produce the centripetal acceleration. The second law gives this net force as the product of the object’s mass m and its acceleration v 2 /r. The net force causing the centripetal acceleration is called the centripetal force F c and points in the same direction as the acceleration — that is, towards the centre of the circle. Centripetal force Magnitude: The centripetal force is the name given to the net force required to keep an object of mass m, moving at a speed v, on a circular path of radius r, and it has a magnitude of F c = mv 2 r (5.3) Direction: The centripetal force always points towards the centre of the circle and continually changes direction as the object moves. The phrase ‘centripetal force’ does not denote a new and separate force created by nature. The phrase merely labels the net force pointing towards the centre of the circular path, and this net force is the vector sum of all the force components that point along the radial direction. Sometimes the centripetal force consists of a single force such as tension (see example 5), friction (see example 7), the normal force or a component thereof (see examples 8 and 13), or the gravitational force (see examples 9–11). However, there are circumstances when a number of different forces contribute simultaneously to the centripetal force (see section 5.7). In some cases, it is easy to identify the source of the centripetal force, as when a model aeroplane on a guideline flies in a horizontal circle.
eBook - PDF- John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler(Authors)
- 2021(Publication Date)
- Wiley(Publisher)
The phrase “centripetal force” does not denote a new and separate force created by nature. The phrase merely labels the net force pointing toward the center of the circular path, and this net force is the vector sum of all the force components that point along the radial direction. Sometimes the centripetal force consists of a single force such as tension (see Example 5), friction (see Example 7), the normal force or a component thereof (see Examples 9 and 14), or the gravitational force (see Examples 10–12). However, there are circumstances when a number of different forces contribute simultaneously to the cen- tripetal force (see Section 5.7). In some cases, it is easy to identify the source of the centripetal force, as when a model airplane on a guideline flies in a horizontal circle. The only force pulling the plane inward is the tension in the line, so this force alone (or a component of it) is the centripe- tal force. Example 5 illustrates the fact that higher speeds require greater tensions. N S W E 1 2 A B C D E CYU FIGURE 5.2 CYU FIGURE 5.1 136 CHAPTER 5 Dynamics of Uniform Circular Motion Conceptual Example 6 deals with another case where it is easy to identify the source of the centripetal force. EX AMPLE 5 The Effect of Speed on Centripetal Force The model airplane in Figure 5.6 has a mass of 0.90 kg and moves at a constant speed on a circle that is parallel to the ground. The path of the airplane and its guideline lie in the same horizontal plane, because the weight of the plane is balanced by the lift gener- ated by its wings. Find the tension in the guideline (length = 17 m) for speeds of 19 and 38 m/s. Reasoning Since the plane flies on a circular path, it experi- ences a centripetal acceleration that is directed toward the center of the circle. According to Newton’s second law of motion, this acceleration is produced by a net force that acts on the plane, and this net force is called the centripetal force.
eBook - PDF- Raymond Serway, Chris Vuille(Authors)
- 2017(Publication Date)
- Cengage Learning EMEA(Publisher)
The force of tension in the string of a yo-yo whirling in a vertical circle is an example of a centripetal force, as is the force of gravity on a satellite circling the Earth. Consider a puck of mass m that is tied to a string of length r and is being whirled at constant speed in a horizontal circular path, as illustrated in Figure 7.9. Its weight is supported by a frictionless table. Why does the puck move in a circle? Because of its inertia, the tendency of the puck is to move in a straight line; however, the string prevents motion along a straight line by exerting a radial force on the puck—a ten- sion force—that makes it follow the circular path. The tension T S is directed along the string toward the center of the circle, as shown in the figure. In general, converting Newton’s second law to polar coordinates yields an equa- tion relating the net centripetal force, F c , which is the sum of the radial compo- nents of all forces acting on a given object, to the centripetal acceleration. The magnitude of the net centripetal force equals the mass times the magnitude of the centripetal acceleration: F 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 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.
eBook - PDF- David Halliday, Robert Resnick, Jearl Walker(Authors)
- 2020(Publication Date)
- Wiley(Publisher)
In the orbiting shuttle, however, you are floating around with no sensation of any force acting on you. Why this difference? The difference is due to the nature of the two centripetal forces. In the car, the centripetal force is the push on the part of your body touching the car wall. You can sense the compression on that part of your body. In the shuttle, the centripetal force is Earth’s gravitational pull on every atom of your body. Thus, there is no compression (or pull) on any one part of your body and no sensation of a force acting on you. (The sensation is said to be one of “weight- lessness,” but that description is tricky. The pull on you by Earth has certainly not disappeared and, in fact, is only a little less than it would be with you on the ground.) Another example of a centripetal force is shown in Fig. 6-8. There a hockey puck moves around in a circle at constant speed v while tied to a string looped around a central peg. This time the centripetal force is the radially inward pull on the puck from the string. Without that force, the puck would slide off in a straight line instead of moving in a circle. Note again that a centripetal force is not a new kind of force. The name merely indicates the direction of the force. It can, in fact, be a frictional force, a gravitational force, the force from a car wall or a string, or any other force. For any situation: Figure 6-8 An overhead view of a hockey puck moving with constant speed v in a circular path of radius R on a horizontal frictionless surface. The centripetal force on the puck is T → , the pull from the string, directed inward along the radial axis r extending through the puck. String Puck R v r T The puck moves in uniform circular motion only because of a toward-the- center force. From Newton’s second law and Eq. 6-17 (a = v 2 /R), we can write the magnitude F of a centripetal force (or a net centripetal force) as F = m v 2 R (magnitude of centripetal force).
- Jerry D. Wilson, Anthony J. Buffa, Bo Lou(Authors)
- 2022(Publication Date)
- CRC Press(Publisher)
FOLLOW-UP EXERCISE. If you swing a ball in a horizontal circle about your head, can the string be exactly horizontal? (See Figure 7.12a.) Explain your answer. [Hint: Analyze the forces acting on the ball.] Keep in mind that, in general, a net force applied at an angle to the direction of motion of an object produces changes in the mag- nitude and direction of the velocity. However, when a net force of constant magnitude is continuously applied at an angle of 90° to the direction of motion (as is centripetal force), only the direction of the velocity changes. This is because there is no force component parallel to the velocity. Also notice that because the centripetal force is always perpendicular to the direction of motion, this force does no work. (Why?) Therefore, a centripetal force does not change the kinetic energy or speed of the object. Note that the centripetal force in the form F c = mv 2 / r is not a new individual force, but rather the cause of the centripetal acceleration, and is supplied by either a real force or the vector sum of several forces. The force supplying the centripetal acceleration for satellites is gravity. In Conceptual Example 7.6, it was the tension in the string. Another force that often supplies centripetal acceleration is friction. Suppose that an automobile moves into a level, circu- lar curve. To negotiate the curve, the car must have a centripetal acceleration, which is supplied by the force of friction between the tires and the road. However, this static friction (why static?) has a maximum limiting value. If the speed of the car is high enough or the curve is sharp enough, the friction will not be sufficient to sup- ply the necessary centripetal acceleration, and the car will skid outward from the center of the curve. If the car moves onto a wet or icy spot, the friction between the tires and the road may be reduced, allowing the car to skid at an even lower speed.
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: .
- 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.
- Paul Anthony Russell(Author)
- 2021(Publication Date)
- Reeds(Publisher)
NEWTON’S FIRST LAW OF MOTION states that every object will continue in a state of rest or in uniform motion, in a straight line, unless acted upon by an external, unbalanced force. However, if a stone is connected to the end of a piece of string and whirled around in a circular path, an inward pull must be continuously exerted to keep it travelling in a circle. The stone itself is exerting an outward radial pull, trying to get move away from the centre and continue on a straight path. If the speed is increased, the force becomes greater until the string reaches its breaking point and snaps; the stone then flies off in a straight line at a tangent to the circle determined by the moment at the time of failure of the string. This can also be demonstrated by swinging a weight in a circle on the end of a string. When up to speed, if the string is released, the weight flies off dragging the string along. The outward radial force created by a body travelling in a circular path, due to its natural tendency to stay in a straight line as stated in Newton’s first law, is termed the centrifugal force. The inward pull applied to counteract the centrifugal force and keep the object on its circular path is termed the centripetal force; it is equal in magnitude to the centrifugal force and opposite in direction, as stated by Newton’s third law of motion. Consider a body moving at a constant speed of v around a circle of radius r. Referring to Figure 5.1, at the instant it is passing point a its instantaneous velocity is v in the direction tangential to the circle at the point a; a little further around the circle it is passing point b and its velocity is now v tangential to the circle at point b. Although the speed is constant, the velocity has changed because there has been a change of direction. If the movement from a to b is through a small angle θ, then to find the change of velocity, the vector diagram of velocities is drawn (Figure 5.1).
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.
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.
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