Conservation of Angular Momentum
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Glossary Physics (I-Introduction)
1 Glossary Physics (I-introduction) - Efficiency: The percent of the work put into a machine that is converted into useful work output; = work done / energy used [-]. = eta In machines: The work output of any machine cannot exceed the work input (<=100%); in an ideal machine, where no energy is transformed into heat: work(input) = work(output), =100%. Energy: The property of a system that enables it to do work. Conservation o. E.: Energy cannot be created or destroyed; it may be transformed from one form into another, but the total amount of energy never changes. Equilibrium: The state of an object when not acted upon by a net force or net torque; an object in equilibrium may be at rest or moving at uniform velocity - not accelerating. Mechanical E.: The state of an object or system of objects for which any impressed forces cancels to zero and no acceleration occurs. Dynamic E.: Object is moving without experiencing acceleration. Static E.: Object is at rest.F Force: The influence that can cause an object to be accelerated or retarded; is always in the direction of the net force, hence a vector quantity; the four elementary forces are: Electromagnetic F.: Is an attraction or repulsion G, gravit. const.6.672E-11[Nm2/kg2] between electric charges: d, distance [m] 2 2 2 2 F = 1/(40) (q1q2/d ) [(CC/m )(Nm /C )] = [N] m,M, mass [kg] Gravitational F.: Is a mutual attraction between all masses: q, charge [As] [C] 2 2 2 2 F = GmM/d [Nm /kg kg 1/m ] = [N] 0, dielectric constant Strong F.: (nuclear force) Acts within the nuclei of atoms: 8.854E-12 [C2/Nm2] [F/m] 2 2 2 2 2 F = 1/(40) (e /d ) [(CC/m )(Nm /C )] = [N] , 3.14 [-] Weak F.: Manifests itself in special reactions among elementary e, 1.60210 E-19 [As] [C] particles, such as the reaction that occur in radioactive decay. -
Rotational Motion (The Dynamics of a Rigid Body)
University of Nebraska - Lincoln DigitalCommons@University of Nebraska - Lincoln Robert Katz Publications Research Papers in Physics and Astronomy 1-1958 Physics, Chapter 11: Rotational Motion (The Dynamics of a Rigid Body) Henry Semat City College of New York Robert Katz University of Nebraska-Lincoln, [email protected] Follow this and additional works at: https://digitalcommons.unl.edu/physicskatz Part of the Physics Commons Semat, Henry and Katz, Robert, "Physics, Chapter 11: Rotational Motion (The Dynamics of a Rigid Body)" (1958). Robert Katz Publications. 141. https://digitalcommons.unl.edu/physicskatz/141 This Article is brought to you for free and open access by the Research Papers in Physics and Astronomy at DigitalCommons@University of Nebraska - Lincoln. It has been accepted for inclusion in Robert Katz Publications by an authorized administrator of DigitalCommons@University of Nebraska - Lincoln. 11 Rotational Motion (The Dynamics of a Rigid Body) 11-1 Motion about a Fixed Axis The motion of the flywheel of an engine and of a pulley on its axle are examples of an important type of motion of a rigid body, that of the motion of rotation about a fixed axis. Consider the motion of a uniform disk rotat ing about a fixed axis passing through its center of gravity C perpendicular to the face of the disk, as shown in Figure 11-1. The motion of this disk may be de scribed in terms of the motions of each of its individual particles, but a better way to describe the motion is in terms of the angle through which the disk rotates. -
Velocity-Corrected Area Calculation SCIEX PA 800 Plus Empower
Velocity-corrected area calculation: SCIEX PA 800 Plus Empower Driver version 1.3 vs. 32 Karat™ Software Firdous Farooqui1, Peter Holper1, Steve Questa1, John D. Walsh2, Handy Yowanto1 1SCIEX, Brea, CA 2Waters Corporation, Milford, MA Since the introduction of commercial capillary electrophoresis (CE) systems over 30 years ago, it has been important to not always use conventional “chromatography thinking” when using CE. This is especially true when processing data, as there are some key differences between electrophoretic and chromatographic data. For instance, in most capillary electrophoresis separations, peak area is not only a function of sample load, but also of an analyte’s velocity past the detection window. In this case, early migrating peaks move past the detection window faster than later migrating peaks. This creates a peak area bias, as any relative difference in an analyte’s migration velocity will lead to an error in peak area determination and relative peak area percent. To help minimize Figure 1: The PA 800 Plus Pharmaceutical Analysis System. this bias, peak areas are normalized by migration velocity. The resulting parameter is commonly referred to as corrected peak The capillary temperature was maintained at 25°C in all area or velocity corrected area. separations. The voltage was applied using reverse polarity. This technical note provides a comparison of velocity corrected The following methods were used with the SCIEX PA 800 Plus area calculations using 32 Karat™ and Empower software. For Empower™ Driver v1.3: both, standard processing methods without manual integration were used to process each result. For 32 Karat™ software, IgG_HR_Conditioning: conditions the capillary Caesar integration1 was turned off. -
The Origins of Velocity Functions
The Origins of Velocity Functions Thomas M. Humphrey ike any practical, policy-oriented discipline, monetary economics em- ploys useful concepts long after their prototypes and originators are L forgotten. A case in point is the notion of a velocity function relating money’s rate of turnover to its independent determining variables. Most economists recognize Milton Friedman’s influential 1956 version of the function. Written v = Y/M = v(rb, re,1/PdP/dt, w, Y/P, u), it expresses in- come velocity as a function of bond interest rates, equity yields, expected inflation, wealth, real income, and a catch-all taste-and-technology variable that captures the impact of a myriad of influences on velocity, including degree of monetization, spread of banking, proliferation of money substitutes, devel- opment of cash management practices, confidence in the future stability of the economy and the like. Many also are aware of Irving Fisher’s 1911 transactions velocity func- tion, although few realize that it incorporates most of the same variables as Friedman’s.1 On velocity’s interest rate determinant, Fisher writes: “Each per- son regulates his turnover” to avoid “waste of interest” (1963, p. 152). When rates rise, cashholders “will avoid carrying too much” money thus prompting a rise in velocity. On expected inflation, he says: “When...depreciation is anticipated, there is a tendency among owners of money to spend it speedily . the result being to raise prices by increasing the velocity of circulation” (p. 263). And on real income: “The rich have a higher rate of turnover than the poor. They spend money faster, not only absolutely but relatively to the money they keep on hand. -
Influence of Angular Velocity of Pedaling on the Accuracy of The
Research article 2018-04-10 - Rev08 Influence of Angular Velocity of Pedaling on the Accuracy of the Measurement of Cyclist Power Abstract Almost all cycling power meters currently available on the The miscalculation may be—even significantly—greater than we market are positioned on rotating parts of the bicycle (pedals, found in our study, for the following reasons: crank arms, spider, bottom bracket/hub) and, regardless of • the test was limited to only 5 cyclists: there is no technical and construction differences, all calculate power on doubt other cyclists may have styles of pedaling with the basis of two physical quantities: torque and angular velocity greater variations of angular velocity; (or rotational speed – cadence). Both these measures vary only 2 indoor trainer models were considered: other during the 360 degrees of each revolution. • models may produce greater errors; The torque / force value is usually measured many times during slopes greater than 5% (the only value tested) may each rotation, while the angular velocity variation is commonly • lead to less uniform rotations and consequently neglected, considering only its average value for each greater errors. revolution (cadence). It should be noted that the error observed in this analysis This, however, introduces an unpredictable error into the power occurs because to measure power the power meter considers calculation. To use the average value of angular velocity means the average angular velocity of each rotation. In power meters to consider each pedal revolution as perfectly smooth and that use this type of calculation, this error must therefore be uniform: but this type of pedal revolution does not exist in added to the accuracy stated by the manufacturer. -
Kinematics Study of Motion
Kinematics Study of motion Kinematics is the branch of physics that describes the motion of objects, but it is not interested in its causes. Itziar Izurieta (2018 october) Index: 1. What is motion? ............................................................................................ 1 1.1. Relativity of motion ................................................................................................................................ 1 1.2.Frame of reference: Cartesian coordinate system ....................................................................................................................................................................... 1 1.3. Position and trajectory .......................................................................................................................... 2 1.4.Travelled distance and displacement ....................................................................................................................................................................... 3 2. Quantities of motion: Speed and velocity .............................................. 4 2.1. Average and instantaneous speed ............................................................ 4 2.2. Average and instantaneous velocity ........................................................ 7 3. Uniform linear motion ................................................................................. 9 3.1. Distance-time graph .................................................................................. 10 3.2. Velocity-time -
1 Euclidean Vector Space and Euclidean Affi Ne Space
Profesora: Eugenia Rosado. E.T.S. Arquitectura. Euclidean Geometry1 1 Euclidean vector space and euclidean a¢ ne space 1.1 Scalar product. Euclidean vector space. Let V be a real vector space. De…nition. A scalar product is a map (denoted by a dot ) V V R ! (~u;~v) ~u ~v 7! satisfying the following axioms: 1. commutativity ~u ~v = ~v ~u 2. distributive ~u (~v + ~w) = ~u ~v + ~u ~w 3. ( ~u) ~v = (~u ~v) 4. ~u ~u 0, for every ~u V 2 5. ~u ~u = 0 if and only if ~u = 0 De…nition. Let V be a real vector space and let be a scalar product. The pair (V; ) is said to be an euclidean vector space. Example. The map de…ned as follows V V R ! (~u;~v) ~u ~v = x1x2 + y1y2 + z1z2 7! where ~u = (x1; y1; z1), ~v = (x2; y2; z2) is a scalar product as it satis…es the …ve properties of a scalar product. This scalar product is called standard (or canonical) scalar product. The pair (V; ) where is the standard scalar product is called the standard euclidean space. 1.1.1 Norm associated to a scalar product. Let (V; ) be a real euclidean vector space. De…nition. A norm associated to the scalar product is a map de…ned as follows V kk R ! ~u ~u = p~u ~u: 7! k k Profesora: Eugenia Rosado, E.T.S. Arquitectura. Euclidean Geometry.2 1.1.2 Unitary and orthogonal vectors. Orthonormal basis. Let (V; ) be a real euclidean vector space. De…nition. -
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. -
Introduction to Robotics Lecture Note 5: Velocity of a Rigid Body
ECE5463: Introduction to Robotics Lecture Note 5: Velocity of a Rigid Body Prof. Wei Zhang Department of Electrical and Computer Engineering Ohio State University Columbus, Ohio, USA Spring 2018 Lecture 5 (ECE5463 Sp18) Wei Zhang(OSU) 1 / 24 Outline Introduction • Rotational Velocity • Change of Reference Frame for Twist (Adjoint Map) • Rigid Body Velocity • Outline Lecture 5 (ECE5463 Sp18) Wei Zhang(OSU) 2 / 24 Introduction For a moving particle with coordinate p(t) 3 at time t, its (linear) velocity • R is simply p_(t) 2 A moving rigid body consists of infinitely many particles, all of which may • have different velocities. What is the velocity of the rigid body? Let T (t) represent the configuration of a moving rigid body at time t.A • point p on the rigid body with (homogeneous) coordinate p~b(t) and p~s(t) in body and space frames: p~ (t) p~ ; p~ (t) = T (t)~p b ≡ b s b Introduction Lecture 5 (ECE5463 Sp18) Wei Zhang(OSU) 3 / 24 Introduction Velocity of p is d p~ (t) = T_ (t)p • dt s b T_ (t) is not a good representation of the velocity of rigid body • - There can be 12 nonzero entries for T_ . - May change over time even when the body is under a constant velocity motion (constant rotation + constant linear motion) Our goal is to find effective ways to represent the rigid body velocity. • Introduction Lecture 5 (ECE5463 Sp18) Wei Zhang(OSU) 4 / 24 Outline Introduction • Rotational Velocity • Change of Reference Frame for Twist (Adjoint Map) • Rigid Body Velocity • Rotational Velocity Lecture 5 (ECE5463 Sp18) Wei Zhang(OSU) 5 / 24 Illustrating -
Basement Flood Mitigation
1 Mitigation refers to measures taken now to reduce losses in the future. How can homeowners and renters protect themselves and their property from a devastating loss? 2 There are a range of possible causes for basement flooding and some potential remedies. Many of these low-cost options can be factored into a family’s budget and accomplished over the several months that precede storm season. 3 There are four ways water gets into your basement: Through the drainage system, known as the sump. Backing up through the sewer lines under the house. Seeping through cracks in the walls and floor. Through windows and doors, called overland flooding. 4 Gutters can play a huge role in keeping basements dry and foundations stable. Water damage caused by clogged gutters can be severe. Install gutters and downspouts. Repair them as the need arises. Keep them free of debris. 5 Channel and disperse water away from the home by lengthening the run of downspouts with rigid or flexible extensions. Prevent interior intrusion through windows and replace weather stripping as needed. 6 Many varieties of sturdy window well covers are available, simple to install and hinged for easy access. Wells should be constructed with gravel bottoms to promote drainage. Remove organic growth to permit sunlight and ventilation. 7 Berms and barriers can help water slope away from the home. The berm’s slope should be about 1 inch per foot and extend for at least 10 feet. It is important to note permits are required any time a homeowner alters the elevation of the property. -
Simple Harmonic Motion
[SHIVOK SP211] October 30, 2015 CH 15 Simple Harmonic Motion I. Oscillatory motion A. Motion which is periodic in time, that is, motion that repeats itself in time. B. Examples: 1. Power line oscillates when the wind blows past it 2. Earthquake oscillations move buildings C. Sometimes the oscillations are so severe, that the system exhibiting oscillations break apart. 1. Tacoma Narrows Bridge Collapse "Gallopin' Gertie" a) http://www.youtube.com/watch?v=j‐zczJXSxnw II. Simple Harmonic Motion A. http://www.youtube.com/watch?v=__2YND93ofE Watch the video in your spare time. This professor is my teaching Idol. B. In the figure below snapshots of a simple oscillatory system is shown. A particle repeatedly moves back and forth about the point x=0. Page 1 [SHIVOK SP211] October 30, 2015 C. The time taken for one complete oscillation is the period, T. In the time of one T, the system travels from x=+x , to –x , and then back to m m its original position x . m D. The velocity vector arrows are scaled to indicate the magnitude of the speed of the system at different times. At x=±x , the velocity is m zero. E. Frequency of oscillation is the number of oscillations that are completed in each second. 1. The symbol for frequency is f, and the SI unit is the hertz (abbreviated as Hz). 2. It follows that F. Any motion that repeats itself is periodic or harmonic. G. If the motion is a sinusoidal function of time, it is called simple harmonic motion (SHM). -
Position, Displacement, Velocity Big Picture
Position, Displacement, Velocity Big Picture I Want to know how/why things move I Need a way to describe motion mathematically: \Kinematics" I Tools of kinematics: calculus (rates) and vectors (directions) I Chapters 2, 4 are all about kinematics I First 1D, then 2D/3D I Main ideas: position, velocity, acceleration Language is crucial Physics uses ordinary words but assigns specific technical meanings! WORD ORDINARY USE PHYSICS USE position where something is where something is velocity speed speed and direction speed speed magnitude of velocity vec- tor displacement being moved difference in position \as the crow flies” from one instant to another Language, continued WORD ORDINARY USE PHYSICS USE total distance displacement or path length traveled path length trav- eled average velocity | displacement divided by time interval average speed total distance di- total distance divided by vided by time inter- time interval val How about some examples? Finer points I \instantaneous" velocity v(t) changes from instant to instant I graphically, it's a point on a v(t) curve or the slope of an x(t) curve I average velocity ~vavg is not a function of time I it's defined for an interval between instants (t1 ! t2, ti ! tf , t0 ! t, etc.) I graphically, it's the \rise over run" between two points on an x(t) curve I in 1D, vx can be called v I it's a component that is positive or negative I vectors don't have signs but their components do What you need to be able to do I Given starting/ending position, time, speed for one or more trip legs, calculate average