DOCSLIB.ORG

Uniform Circular Motion

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Uniform Circular Motion Uniform Circular Motion Part I. The Centripetal Impulse The “centripetal impulse” was Sir Isaac Newton’ favorite force. The Polygon Approximation. Newton made a business of analyzing the motion of bodies in circular orbits, or on any curved path, as motion on a polygon. Straight lines are easier to handle than circular arcs. The following pictures show how an inscribed or circumscribed polygon approximates a circular path. The approximation gets better as the number of sides of the polygon increases. To keep a body moving along a circular path at constant speed, a force of constant magnitude that is always directed toward the center of the circle must be applied to the body at all times. To keep the body moving on a polygon at constant speed, a sequence of impulses (quick hits), each directed toward the center, must be applied to the body only at those points on the path where there is a bend in the straight- line motion. The force Fc causing uniform circular motion and the force Fp causing uniform polygonal motion are both centripetal forces: “center seeking” forces that change the direction of the velocity but not its magnitude. A graph of the magnitudes of Fc and Fp as a function of time would look as follows: Force F p causing Polygon Motion Force Force F c causing Circular Motion time In essence, Fp is the “digital version ” of Fc . Imagine applying an “on-off force” to a ball rolling on the table − one hit every nanosecond – in a direction perpendicular to the motion. By moving around one billion small bends (polygon corners) per second, the ball will appear to move on perfect circle. 1 Applying a Centripetal Impulse Here you will get a kinesthetic sense of Newton’s favorite force. Your team will learn what it “feels like” to apply the force Fp that causes a ball to move on a polygon. The bent-line polygonal path pictured below and the circular arc it approximates appear on a sheet of paper at your table. Ìʌʌľ¿ Ìʌʌľ¼ DO NOT tape this sheet to the table. USE CAUTION so heavy ball does not roll off table onto floor/foot. For a ball moving at constant speed along the left line in the picture, how do you get the ball to suddenly turn the corner or “round the bend” and end up moving at the same constant speed on the right line? • Let the ball roll down the ramp onto the arrow (initial velocity vector) that leads into the polygon segment (bold straight line). Assume the speed of the ball is constant along the line, i.e. neglect friction. • When the ball reaches the bend, use the force-probe tip to apply one “quick hit” to the ball so that the ball successfully rounds the bend − but does not noticeably change its speed. The direction of your hit is crucial – this special direction is a huge part of the physics of circular motion! Do not record the force. The probe is used here simply as a pushing device. Learning how to push is your quest. • The speed of the ball should not be too fast (so that it is difficult to push) or too slow (so that friction noticeably slows the ball). Try different speeds by varying the initial location of the ball on the ramp until you find a speed that is just right – the “optimal speed”. Remember this optimal initial location because you will use it in future parts of this lab. • Practice the push (polygonal impulse) several times until you get a feel for the magnitude , the duration , and the direction of the push. All team members should give it a try. After your team has discovered the optimal speed and the correct push, summarize your findings in the space below. Draw a picture that shows the path of the ball, the force vector , and the acceleration ̀ľ+ vector of the ball. Estimate the magnitude (maximum value) and the duration (how long it lasts) of ͕ľ your push − this is a rough estimate since it is based solely on what you felt while pushing. Magnitude of ≈ _____ N. ̀ľ+ Duration of ≈ _____ s. ̀ľ+ *Before you move on to the next part, ask your lab instructor to check your pushing technique* 2 Part II. Measuring Centripetal Impulse and Momentum Change Impulse-Momentum Theorem. Newton’s law of motion can be written as ľ or ̀ͨ͘ = ͪ͘͡ľ ǹ ̀ľͨ͘ = ͪ͡ľ! − ͪ͡ľ$ . This relation says , where impulse is and momentum is . Impulse measures ̈́ľ = ∆ͤľ ̈́ľ ≡ Ȅ ̀ľͨ͘ ͤľ ≡ ͪ͡ľ both the strength and the duration of the force. Note that , where is the average of F Ȅ ̀ͨ͘ = ̀Ŭ ∆ͨ ̀Ŭ over the time interval ∆t during which F acts. The impulse-momentum theorem reveals a wonderful relation between “force × time area” and “momentum change”: F(t) ̻͙͕ͦ = ̀Ŭ∆ͨ = ∆ͤ Area under F (t) Curve = Change in Momentum ̀Ŭ t ∆t Measuring the Impulse Jp 1. Open Logger Pro file “Force Probe”. Go to Experiment, Data Collection, change the “Sampling Rate” to 200 samples per second. ZERO the force probe while it is in the horizontal position. 2. Start the ball from its optimal location on the ramp – the place that gets you the best speed. Let the ball roll down the ramp and onto the arrow that leads into the polygon segment. 3. Apply Fp so that the ball turns the corner but does not noticeably change its speed. 4. Change the scales on the Force vs Time graph so that the shape (height and width) of the “triangular force spike” is clearly displayed. 5. Compute the impulse Jp of your force-probe hit Fp by highlighting the force spike on you graph and clicking on the area icon . Record the value of Jp in the table below. 6. Find the average force (use the STATS button) and the duration time ∆tp. Enter their values in the ̀Ŭ+ table. Their product should be equal to Jp. 7. Do four more trials. Start with the ball at the same initial location on the ramp each time so that the speed of the ball is the same each trial. Average your Jp values. Find the uncertainty (half-width spread). Trial 1 2 3 4 5 Average Force ̀ŭ+ Duration Time ∆tp Impulse Jp Jp = __________ ± __________ Ns . 3 Measuring the Momentum Change ∆∆∆p The velocity vectors of the ball along the two polygon lines are drawn below. Note that is also the ͪľ$ velocity of the ball when it enters the circular arc while is the velocity when it exits. ͪľ! y ͪľ$ ͪľ! θ θ x θ θ 1. Use this diagram to calculate the change in the velocity vector: . ∆ͪľ ≡ ͪľ! − ͪľ$ Hint: Express each velocity vector in terms of its x and y components and then subtract the vectors. Show your vector algebra in the space above. Express your answer in terms of the variables v and θ, where v is the constant speed of the ball: , and θ is the angle defined in the diagram. ͪ = |ͪľ$| = ɳͪľ!ɳ ________________ . ͪľ! − ͪľ$ = 2. How is the direction of related to the direction of ? ∆ͪľ ̀ľ+ 3. Measure the mass m of the ball and the angle θ: m = ________ kg. θ = ________ . 4. Measure the speed v of the ball as follows. Place the ball at its optimal initial position on the ramp. Place the short ruler near the end of the ramp so that when the ball rolls off the ramp onto the table, the ball moves alongside the ruler. Measure the time it takes the ball to cover the length of the ruler. Repeat this measurement to make sure you are getting a consistent value for the speed of the ball. Display your data in the space below. v = ____________ m/s . 5. Compute the momentum change. Include the direction. ______________ kg m/s . ∆ͤľ = 4 Does your Experimental Data “Prove” the Theorem ? ¦ľÆ = ∆Æʌʌľ You have measured with a force probe. You have measured with a ruler, protractor, stopwatch, and ̈́ľ+ ∆ͤľ mass scale. Compare the directions of and . Compare their magnitudes. Does ∆p fall within the ̈́ľ+ ∆ͤľ uncertainty range of Jp ? Part III. Centripetal Force Fc “Polygon Formula” for F c . The force acts continuously over the whole circular arc, while the ̀ľ force acts momentarily only at the bend in the polygon. ̀ľ+ Fp Fc Fc Fc Fc Fc Fc Fc F Fc Fc c Fc ∆ Fc Fc tp Fc Fc F c ∆tc The change in the velocity of the ball is the same along the c-path and the p-path because of the way the polygon fits the circle. Thus according to Newton’s law, the relation between Fc and Fp is ̀ ∆ͨ = ̀Ŭ+ ∆ͨ+ In words, a small force acting over the long time ∆tc causes the same momentum change ̀ľ ͪ͡ľ! − ͪ͡ľ$ as a large force acting over the short time ∆tp . ̀ľ+ Comment: This relation is approximate. The exact relation between F c and F p is Ȅ ̀ľ ͨ͘ = ͪ͡ľ! − ͪ͡ľ$ = Ȅ ̀ľ+ ͨ͘ + . The impulse reduces to Fc ∆tc × sin θ/θ (directed downward). The angular factor (sin θ/θ) arises because the Ȅ ̀ľ ͨ͘ direction of along the circular arc does not always point downward, like it does for at the polygon bend. We ̀ľ ̀ľ+ neglect this factor since its value is near unity for the short arcs in this lab. 5 Thus we arrive at an interesting formula for the centripetal force in terms of a centripetal (polygonal) impulse and a circle time: ̀+∆ͨ+ ̈́+ ̀ = ͣͦ ̀ = .
Load more

Recommended publications
  • PHYSICS of ARTIFICIAL GRAVITY Angie Bukley1, William Paloski,2 and Gilles Clément1,3
    Chapter 2 PHYSICS OF ARTIFICIAL GRAVITY Angie Bukley1, William Paloski,2 and Gilles Clément1,3 1 Ohio University, Athens, Ohio, USA 2 NASA Johnson Space Center, Houston, Texas, USA 3 Centre National de la Recherche Scientifique, Toulouse, France This chapter discusses potential technologies for achieving artificial gravity in a space vehicle. We begin with a series of definitions and a general description of the rotational dynamics behind the forces ultimately exerted on the human body during centrifugation, such as gravity level, gravity gradient, and Coriolis force. Human factors considerations and comfort limits associated with a rotating environment are then discussed. Finally, engineering options for designing space vehicles with artificial gravity are presented. Figure 2-01. Artist's concept of one of NASA early (1962) concepts for a manned space station with artificial gravity: a self- inflating 22-m-diameter rotating hexagon. Photo courtesy of NASA. 1 ARTIFICIAL GRAVITY: WHAT IS IT? 1.1 Definition Artificial gravity is defined in this book as the simulation of gravitational forces aboard a space vehicle in free fall (in orbit) or in transit to another planet. Throughout this book, the term artificial gravity is reserved for a spinning spacecraft or a centrifuge within the spacecraft such that a gravity-like force results. One should understand that artificial gravity is not gravity at all. Rather, it is an inertial force that is indistinguishable from normal gravity experience on Earth in terms of its action on any mass. A centrifugal force proportional to the mass that is being accelerated centripetally in a rotating device is experienced rather than a gravitational pull.
    [Show full text]
  • Centripetal Force Is Balanced by the Circular Motion of the Elctron Causing the Centrifugal Force
    STANDARD SC1 b. Construct an argument to support the claim that the proton (and not the neutron or electron) defines the element’s identity. c. Construct an explanation based on scientific evidence of the production of elements heavier than hydrogen by nuclear fusion. d. Construct an explanation that relates the relative abundance of isotopes of a particular element to the atomic mass of the element. First, we quickly review pre-requisite concepts One of the most curious observations with atoms is the fact that there are charged particles inside the atom and there is also constant spinning and Warm-up 1: List the name, charge, mass, and location of the three subatomic circling. How does atom remain stable under these conditions? Remember particles Opposite charges attract each other; Like charges repel each other. Your Particle Location Charge Mass in a.m.u. Task: Read the following information and consult with your teacher as STABILITY OF ATOMS needed, answer Warm-Up tasks 2 and 3 on Page 2. (3) Death spiral does not occur at all! This is because the centripetal force is balanced by the circular motion of the elctron causing the centrifugal force. The centrifugal force is the outward force from the center to the circumference of the circle. Electrons not only spin on their own axis, they are also in a constant circular motion around the nucleus. Despite this terrific movement, electrons are very stable. The stability of electrons mainly comes from the electrostatic forces of attraction between the nucleus and the electrons. The electrostatic forces are also known as Coulombic Forces of Attraction.
    [Show full text]
  • Measuring Inertial, Centrifugal, and Centripetal Forces and Motions The
    Measuring Inertial, Centrifugal, and Centripetal Forces and Motions Many people are quite confused about the true nature and dynamics of cen- trifugal and centripetal forces. Some believe that centrifugal force is a fictitious radial force that can’t be measured. Others claim it is a real force equal and opposite to measured centripetal force. It is sometimes thought to be a continu- ous positive acceleration like centripetal force. Crackpot theorists ignore all measurements and claim the centrifugal force comes out of the aether or spa- cetime continuum surrounding a spinning body. The true reality of centripetal and centrifugal forces can be easily determined by simply measuring them with accelerometers rather than by imagining metaphysical assumptions. The Momentum and Energy of the Cannon versus a Cannonball Cannon Ball vs Cannon Momentum and Energy Force = mass x acceleration ma = Momentum = mv m = 100 kg m = 1 kg v = p/m = 1 m/s v = p/m = 100 m/s p = mv 100 p = mv = 100 energy = mv2/2 = 50 J energy = mv2/2 = 5,000 J Force p = mv = p = mv p=100 Momentum p = 100 Energy mv2/2 = mv2 = mv2/2 Cannon ball has the same A Force always produces two momentum as the cannon equal momenta but it almost but has 100 times more never produces two equal kinetic energy. quantities of kinetic energy. In the following thought experiment with a cannon and golden cannon ball, their individual momentum is easy to calculate because they are always equal. However, the recoil energy from the force of the gunpowder is much greater for the ball than the cannon.
    [Show full text]
  • Centripetal Force Purpose: in This Lab We Will Study the Relationship
    Centripetal Force Purpose: In this lab we will study the relationship between acceleration of an object moving with uniform circular motion and the force required to produce that acceleration. Introduction: An object moving in a circle with constant tangential speed is said to be executing uniform circular motion. This results from having a net force directed toward the center of the circular path. This net force, the centripetal force, gives rise to a centripetal acceleration toward the center of the circular path, and this changes the direction of the motion of the object continuously to make the circular path possible. The equation which governs rotational dynamics is Fc = mac, where Fc is the centripetal force, ac is the centripetal acceleration, and m is the mass of the object. This is nothing but Newton's second law in the v2 radial direction! From rotational kinematics we can show that ac= r , where v is the tangential speed and mv2 r is the radius of the circular path. By combining the two equations, we get Fc = r . The period T of circular motion is the time it takes for the object to make one complete revolution. The tangential speed v of 2πr the object is v = T , which is the distance traveled divided by the time elapsed (i.e. circumference/period). Thus we finally get: 4π2mr F = c T 2 In this laboratory session we will keep the centripetal force Fc and the mass m constant and vary the radius r. We will investigate how the period T need be adjusted as the radius r is changed.
    [Show full text]
  • Chapter 13: the Conditions of Rotary Motion
    Chapter 13 Conditions of Rotary Motion KINESIOLOGY Scientific Basis of Human Motion, 11 th edition Hamilton, Weimar & Luttgens Presentation Created by TK Koesterer, Ph.D., ATC Humboldt State University Revised by Hamilton & Weimar REVISED FOR FYS by J. Wunderlich, Ph.D. Agenda 1. Eccentric Force àTorque (“Moment”) 2. Lever 3. Force Couple 4. Conservation of Angular Momentum 5. Centripetal and Centrifugal Forces ROTARY FORCE (“Eccentric Force”) § Force not in line with object’s center of gravity § Rotary and translatory motion can occur Fig 13.2 Torque (“Moment”) T = F x d F Moment T = F x d Arm F d = 0.3 cos (90-45) Fig 13.3 T = F x d Moment Arm Torque changed by changing length of moment d arm W T = F x d d W Fig 13.4 Sum of Torques (“Moments”) T = F x d Fig 13.8 Sum of Torques (“Moments”) T = F x d § Sum of torques = 0 • A balanced seesaw • Linear motion if equal parallel forces overcome resistance • Rowers Force Couple T = F x d § Effect of equal parallel forces acting in opposite direction Fig 13.6 & 13.7 LEVER § “A rigid bar that can rotate about a fixed point when a force is applied to overcome a resistance” § Used to: – Balance forces – Favor force production – Favor speed and range of motion – Change direction of applied force External Levers § Small force to overcome large resistance § Crowbar § Large Range Of Motion to overcome small resistance § Hitting golf ball § Balance force (load) § Seesaw Anatomical Levers § Nearly every bone is a lever § The joint is fulcrum § Contracting muscles are force § Don’t necessarily resemble
    [Show full text]
  • Chapter 8: Rotational Motion
    TODAY: Start Chapter 8 on Rotation Chapter 8: Rotational Motion Linear speed: distance traveled per unit of time. In rotational motion we have linear speed: depends where we (or an object) is located in the circle. If you ride near the outside of a merry-go-round, do you go faster or slower than if you ride near the middle? It depends on whether “faster” means -a faster linear speed (= speed), ie more distance covered per second, Or - a faster rotational speed (=angular speed, ω), i.e. more rotations or revolutions per second. • Linear speed of a rotating object is greater on the outside, further from the axis (center) Perimeter of a circle=2r •Rotational speed is the same for any point on the object – all parts make the same # of rotations in the same time interval. More on rotational vs tangential speed For motion in a circle, linear speed is often called tangential speed – The faster the ω, the faster the v in the same way v ~ ω. directly proportional to − ω doesn’t depend on where you are on the circle, but v does: v ~ r He’s got twice the linear speed than this guy. Same RPM (ω) for all these people, but different tangential speeds. Clicker Question A carnival has a Ferris wheel where the seats are located halfway between the center and outside rim. Compared with a Ferris wheel with seats on the outside rim, your angular speed while riding on this Ferris wheel would be A) more and your tangential speed less. B) the same and your tangential speed less.
    [Show full text]
  • Conceptual Physics Rotational Motion
    Conceptual Physics Rotational Motion Lana Sheridan De Anza College July 17, 2017 Last time • energy sources discussion • collisions (elastic) Overview • inelastic collisions • circular motion and rotation • centripetal force • fictitious forces • torque • moment of inertia • center of mass • angular momentum Inelastic collisions are collisions in which energy is lost as sound, heat, or in deformations of the colliding objects. When the colliding objects stick together afterwards the collision is perfectly inelastic. Types of Collision There are two different types of collisions: Elastic collisions are collisions in which none of the kinetic energy of the colliding objects is lost. (Ki = Kf ) When the colliding objects stick together afterwards the collision is perfectly inelastic. Types of Collision There are two different types of collisions: Elastic collisions are collisions in which none of the kinetic energy of the colliding objects is lost. (Ki = Kf ) Inelastic collisions are collisions in which energy is lost as sound, heat, or in deformations of the colliding objects. Types of Collision There are two different types of collisions: Elastic collisions are collisions in which none of the kinetic energy of the colliding objects is lost. (Ki = Kf ) Inelastic collisions are collisions in which energy is lost as sound, heat, or in deformations of the colliding objects. When the colliding objects stick together afterwards the collision is perfectly inelastic. Inelastic Collisions For general inelastic collisions, some kinetic energy is lost. But we can still use the conservation of momentum: pi = pf 9.4 Collisions in One Dimension 257 In contrast, the total kinetic energy of the system of particles may or may not be con- served, depending on the type of collision.
    [Show full text]
  • 4. Central Forces
    4. Central Forces In this section we will study the three-dimensional motion of a particle in a central force potential. Such a system obeys the equation of motion mx¨ = V (r)(4.1) r where the potential depends only on r = x .Sincebothgravitationalandelectrostatic | | forces are of this form, solutions to this equation contain some of the most important results in classical physics. Our first line of attack in solving (4.1)istouseangularmomentum.Recallthatthis is defined as L = mx x˙ ⇥ We already saw in Section 2.2.2 that angular momentum is conserved in a central potential. The proof is straightforward: dL = mx x¨ = x V =0 dt ⇥ − ⇥r where the final equality follows because V is parallel to x. r The conservation of angular momentum has an important consequence: all motion takes place in a plane. This follows because L is a fixed, unchanging vector which, by construction, obeys L x =0 · So the position of the particle always lies in a plane perpendicular to L.Bythesame argument, L x˙ =0sothevelocityoftheparticlealsoliesinthesameplane.Inthis · way the three-dimensional dynamics is reduced to dynamics on a plane. 4.1 Polar Coordinates in the Plane We’ve learned that the motion lies in a plane. It will turn out to be much easier if we work with polar coordinates on the plane rather than Cartesian coordinates. For this reason, we take a brief detour to explain some relevant aspects of polar coordinates. To start, we rotate our coordinate system so that the angular momentum points in the z-direction and all motion takes place in the (x, y)plane.Wethendefinetheusual polar coordinates x = r cos ✓, y= r sin ✓ –48– Our goal is to express both the velocity and acceleration y ^ ^ θ r in polar coordinates.
    [Show full text]
  • Centripetal Force
    Centripetal Force Purpose The purpose of this experiment is to empirically determine the relationship between the angular velocity of a body in circular motion and: the centripetal force F necessary to maintain a constant angular velocity the mass M of the body and the radius R of the circular path. Equipment Centripetal force apparatus with cylindrical bob; set of four different springs; three-spring extenders; slotted weights; weight hanger; string, log-log graph paper. Preliminary Discussion In this experiment we will study the motion of a body which is moving in a circle at a constant speed. We will try to deduce a mathematical expression from which you could predict the behavior of any body moving in a circle under the influence of a centripetal force, by conducting a systematic set of experiments and using graphical and computer methods to analyze the results. The parameters which we will be measuring are the mass M and angular velocity ω of the body, the radius R of the circular path, and the force F necessary to keep the body moving in a circular path when the speed is constant. This force is directed towards the center of the circular path and is called a centripetal force. The angular velocity, ω, for circular motion is related to the speed v of the object through the relation, ω = v/R. We will determine the functional dependence of the angular velocity ω on each of the other parameters by performing three experiments. In each experiment one of the parameters will be varied while the other two are held constant, i.e., we will measure ω as a function of: 1.
    [Show full text]
  • Chapter 10 Motion in a Non-Inertial Reference Frame the Laws Of
    Physics 235 Chapter 10 Chapter 10 Motion in a Non-Inertial Reference Frame The laws of physics are only valid in inertial reference frames. However, it is not always easy to express the motion of interest in an inertial reference frame. Consider for example the motion of a book laying on top of a table. In a reference frame that is fixed with respect to the Earth, the motion is simple: if the book is at rest, it will remain at rest (here we assume that the surface of the table is horizontal). However, we do know that the earth frame is not an inertial frame. In order to describe the motion of the book in an inertial frame, we need to take into account the rotation of the Earth around its axis, the rotation of the Earth around the sun, the rotation of our solar system around the center of our galaxy, etc. etc. The motion of the book will all of a sudden be a lot more complicated! For many experiments, the effect of the Earth not being an inertial reference frame is too small to be observed. Other effects, such as the tides, can only be explained if we take into consideration the non-inertial nature of the reference frame of the Earth and apply the laws of physics in an inertial frame. Rotating Coordinate Systems Consider the two coordinate systems shown in Figure 1. The non-primed coordinates are the coordinates in the rotating frame, and the primed coordinates are the coordinates in the fixed coordinate system.
    [Show full text]
  • Chapter VII. Rotating Coordinate Systems
    Chapter VII. Rotating Coordinate Systems 7.1. Frames of References In order to really look at particle dynamics in the context of the atmosphere, we must now deal with the fact that we live and observe the weather in a non-inertial reference frame. Specially, we will look at a rotating coordinate system and introduce the Coriolis and centrifugal force. Rotating and Non-rotating Frames of Reference First, start by recognizing that presence of 2 coordinate systems when dealing with problems related to the earth: a) one fixed to the earth that rotates and is thus accelerating (non-inertial), our real life frame of reference b) one fixed with respect to the remote "star", i.e., an inertial frame where the Newton's laws are valid. Apparent Force In order to apply Newton's laws in our earth reference frame, we must take into account the acceleration of our coordinate system (earth). This leads to the apparent forces that get added to Newton's 2nd law of motion: dVr Fr = real (inertial) (7.1) dtm r dVr Fr F =+real apparent (non-inertial) (7.2) dtmm Fr where apparent are due solely to the fact that we operate / observe in a non-inertial m reference frame. rr dAdA We need to relate to . dtdt inertialnon-inertial 7-1 7.2. Time Derivatives in Fixed and Rotating Coordinates Reading Section 7.1 of Symon. Using concepts developed in the last chapter, let's introduce some notion that will prove to be useful. r W z y Vr r T R r Latitude circle a =colatitude f = latitude x Equatorial Plane Let r = position vector from the origin (center of the earth).
    [Show full text]
  • 11. Kinematics of Angular Motion Rk.Nb
    11. Describing Angular or Circular Motion Introduction Examples of angular motion occur frequently. Examples include the rotation of a bicycle tire, a merry-go-round, a toy top, a food processor, a laboratory centrifuge, and the orbit of the Earth around the Sun. More complicated examples involving rotational motion combined with linear motion include a rolling billiard ball, the tire of a bicycle that is ridden, a rolling pin in the kitchen, etc. However, mostly we will consider only the case of pure rotational motion since it is simpler. Also, again for reasons of simplicity, we will look only at angular motion that has a fixed radius. Keep in mind that there are two kinds of angular motion: rotational motion (e.g., the Earth rotates on its axis once every 24 hours) and revolutionary motion (e.g., the Earth revolves about the Sun and makes one complete cycle in a year). ¢ | £ 2 11. Kinematics of Angular Motion_rk.nb Measuring Angular Distance q 1. The Degree Measure of q (example: 35°, where degree is represented by the symbol °) A. This is the most common way of measuring angular motion. One complete cycle or revolution is divided up into 360 equal bits called degrees. B. The 360 is arbitrary and is kept for historical reasons but any other number could have been chosen, for example, 100. C. Important: Notice that the size of the degree is unrelated to the size of the circle. For a circle of radius r, there are 360° in one revolution or complete trip around the circle. D.
    [Show full text]