DOCSLIB.ORG

Revised Glossary for AQA GCSE Physics Student Book

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Revised Glossary for AQA GCSE Physics Student Book Glossary<H1_EM> absorb take in or soak up, for example energy Afrom sound B absorption<txtGlss_wrd> process <TXT_GLSS> in which matter takes in background radiation nuclear radiation that energy, e.g. when an atom takes in energy from an is present in the environment as a result of the electromagnetic wave radioactive decay of certain elements; it is produced from natural sources (e.g., from radon gas in the acceleration rate at which an object speeds Earth’s crust) and from artificial sources (e.g., as a up, calculated from change in velocity divided result of testing nuclear weapons) by time; symbol a, unit metres per second squared, m/s2 becquerel unit of activity for a radioactive isotope, symbol Bq accuracy how close a measurement is to its true value beta particle fast-moving electron that is emitted by activity the rate at which unstable nuclei decay an atomic nucleus in some types of radioactive decay in a sample of a radioactive material; unit becquerel, Bq Big Bang theory generally accepted explanation for the origin of the universe, which states that the air resistance force produced by the collision of universe began from a very small region that was molecules in air with a moving object; the force acts extremely hot and dense to oppose the direction of movement black body object that absorbs all the radiation that alternating current (a.c.) electric current that falls on it continually changes direction black dwarf star at the end of its life, where no alpha particle a particle (two neutrons and two further nuclear fusion reactions take place and so no protons, same as a helium nucleus) emitted by an light is produced atomic nucleus during radioactive decay boundary line or surface between two different alternator device that produces an alternating media (e.g., the surface between air and glass), current using the generator effect, e.g., from the across which light may be refracted or reflected rotation of a coil in a magnetic field braking distance distance travelled by a vehicle after ammeter device that measures electric current the brakes have been applied before coming to a ampere SI unit of electric current, symbol A; an complete stop electric current of 1 A is equal to 1 C of charge passing through a point in a circuit in 1 s C amplitude maximum displacement of a wave or cancer disease in which uncontrolled division of cells oscillating object from its rest position takes place, forming a tumour; some types of cancer angle of incidence the angle between the incident are caused by the effects of ionising radiation on ray and the normal cells angle of reflection the angle between the reflected cell (electric circuits) circuit component that stores ray and the normal energy in the form of chemical energy a number of electric cells may be joined to form a battery atmospheric pressure force per unit area produced by the weight of air; it decreases as you go higher in cell (living things) smallest structural unit of a living the atmosphere organism; cells may be damaged by some types of ionising radiation atomic number number of protons in the nucleus of an atom of an element centre of mass a single point where the weight of an object can be considered to act attraction force that acts between two objects that tends to draw them closer together, e.g., the force chain reaction occurs when the neutrons released by a that arises between a positive electric charge and a nucleus undergoing fission go on to split more nuclei negative electric charge change of state process in which one state of matter average speed distance travelled by an object over a changes to another, e.g., solid melting to form liquid, measured time interval or gas condensing to form liquid Glossary 301 58774_P298_310.indd 301 11/3/16 12:43 PM Physics circuit diagram visual representation of electrical conservation of momentum a fundamental <H1_EM>components connected by wires, using standard principle of physics: the total momentum of a system symbols of objects after a collision is the same as the total momentum before the collision circuit symbol visual representation of an electrical component; a standard symbol exists for each type contact force force that acts at the point of contact absorbof electrical take componentin or soak up, for example energy between two objects (e.g., friction or the normal from sound reaction) closed system system that is not acted upon by any <txtGlss_wrd>external forces <TXT_GLSS>and does not exchange energy with contamination (radioactivity) the unwanted its surroundings presence of materials containing radioactive atoms commutator (split-ring) electrical connector control variable quantity in an experiment consisting of two semi-circular metal contacts, that is kept constant while the independent which is connected to a rotating coil in a dynamo variable is changed and the dependent variable is (to produce direct current) or a motor (to use direct measured current) convex lens lens that curves outwards with the compass (magnetic) device that shows the direction centre thicker than the edges – it causes light rays to of a magnetic field in which it is placed; typically come together (converge). The image produced by a a compass is made from a magnetised needle or convex lens can be either real or virtual pointer that is free to rotate coulomb SI unit of electric charge, symbol C components (forces) the result of breaking down count rate the number of decays recorded each or resolving a single force into two separate forces second by a detector (e.g. Geiger–Muller tube) acting in perpendicular directions, often horizontally and vertically CT (or CAT) scan scan that takes many X-ray images from different directions to build up a 3D image of compress squashing something into a smaller the body volume – liquids are incompressible: they cannot be squashed current (electric) flow of electric charge; the size of the electric current is the rate of flow of electric compression a region of a sound wave where the charge; symbol I, unit amps (A) particles are closer together concave lens lens that curves inwards with the D centre thinner than the edges – it causes light rays to spread out (diverge). The image produced by a dark energy unknown form of energy which is concave lens is always virtual thought to accelerate the expansion of the universe. conclusion section at the end of a report on an It is estimated to constitute around 68% of the total experiment that summarises how the results support energy in the universe or contradict the original hypothesis dark matter unidentified matter which doesn't reflect conductivity (thermal) quantity that measures the electromagnetic radiation and is thought to constitute rate at which thermal energy is conducted through around 27% of the total mass-energy of the universe a material; the higher the thermal conductivity, the data measurements of quantities in an experiment; higher the rate of thermal energy transfer data can be recorded in a table and used to produce conductor material or object that allows electric graphs charge to flow through it decay (radioactive) process in which the nucleus of conservation of electric charge a fundamental an atom breaks apart and emits radiation principle of physics: electric charge cannot be deceleration negative acceleration, when an object created or destroyed, only transferred from one slows down object to another; the total electric charge of a closed system is constant degrees Celsius unit of temperature, symbol °C; 1 1 °C is of the temperature difference between conservation of energy a fundamental principle of 100 physics: energy cannot be created or destroyed, only the melting point and boiling point of water transferred, stored or dissipated. This means that the density measure of the amount of substance per unit total energy of a closed system is constant. volume; symbol r, unit kilograms per metre cubed, conservation of mass a fundamental principle of kg/m3 physics: mass cannot be created or destroyed by dependent variable quantity in an experiment that physical changes or chemical reactions; the total is measured for each change in the independent mass of a system is constant variable 302 AQA GCSE Physics: Student Book 58774_P298_310.indd 302 11/3/16 12:43 PM diffuse reflection reflection from a rough surface, electric charge fundamental property of matter that so that an incident ray is scattered (reflected at many results in an electric field around an object; objects angles) can be electrically positive, negative or neutral (no overall charge); symbol Q, unit coulomb, C diode circuit component with a low resistance if it is connected one way around in a circuit, or a very high electric current flow of electric charge; the size of the resistance if it is connected the other way around; a electric current is the rate of flow of electric charge; diode allows current in one direction only symbol I, unit amps, A direct current (d.c.) flow of electric charge in one electric field region around an electrically charged direction only object in which a force acts on other electrically charged objects; the objects do not have to touch for directly proportional relationship a relationship the force to act of the form y proportional to (∝) x; plotting a graph of y against x will produce a straight line through electrical power amount of energy transferred each the origin second; symbol P, unit watts or joules per second, W or J/s displacement distance moved in a particular direction; it is a vector quantity and is equal to the
Load more

Recommended publications
  • 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.
    [Show full text]
  • Test of Self-Organization in Beach Cusp Formation Giovanni Coco,1 T
    JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 108, NO. C3, 3101, doi:10.1029/2002JC001496, 2003 Test of self-organization in beach cusp formation Giovanni Coco,1 T. K. Burnet, and B. T. Werner Complex Systems Laboratory, Cecil and Ida Green Institute of Geophysics and Planetary Physics, University of California, San Diego, La Jolla, California, USA Steve Elgar Woods Hole Oceanographic Institution, Woods Hole, Massachusetts, USA Received 4 June 2002; revised 6 November 2002; accepted 13 November 2002; published 29 March 2003. [1] Field observations of swash flow patterns and morphology change are consistent with the hypothesis that beach cusps form by self-organization, wherein positive feedback between swash flow and developing morphology causes initial development of the pattern and negative feedback owing to circulation of flow within beach cusp bays causes pattern stabilization. The self-organization hypothesis is tested using measurements from three experiments on a barrier island beach in North Carolina. Beach cusps developed after the beach was smoothed by a storm and after existing beach cusps were smoothed by a bulldozer. Swash front motions were recorded on video during daylight hours, and morphology was measured by surveying at 3–4 hour intervals. Three signatures of self- organization were observed in all experiments. First, time lags between swash front motions in beach cusp bays and horns increase with increasing relief, representing the effect of morphology on flow. Second, differential erosion between bays and horns initially increases with increasing time lag, representing the effect of flow on morphology change because positive feedback causes growth of beach cusps. Third, after initial growth, differential erosion decreases with increasing time lag, representing the onset of negative feedback that stabilizes beach cusps.
    [Show full text]
  • Leadscrew Brochure
    • High Repeatability • High accuracy • Short Lead times • Fast Prototyping High Precision Lead Screws Offering smooth, precise, cost effective positioning, lead screws are the ideal solution for your application. Thomson Neff precision lead screws from Huco Dynatork are an excellent economical solution for your linear motion requirements. For more than 25 years, Thomson has designed and manufactured the highest quality lead screw assemblies in the industry. Our precision rolling proc- ess ensures accurate positioning to .075mm/300mm and our PTFE coating process produces assemblies that have less drag torque and last longer. Huco Dynatork provides a large array of standard plastic nut assemblies in anti-backlash or standard Supernut® designs. All of our standard plastic nut assemblies use an internally lubricated Acetal providing excellent lubricity and wear resistance with or without additional lubrication. With the introduction of our new unique patented zero backlash designs, Huco Dynatork provides assemblies with high axial stiffness, zero back- lash and the absolute minimum drag torque to reduce motor requirements. These designs produce products that cost less, perform better and last longer. Both designs automatically adjust for wear ensuring zero backlash for the life of the nut. Huco Dynatork also provides engineering design services to aid in your design requirements producing a lead screw assembly to your specifica- tions. Call Huco Dynatork today on 01992 501900 to discuss your application with one of our experienced application engineers Huco Dynatork Products Deliver Performance To ensure precise positioning, the elimination of backlash is of primary concern. Several types of anti-backlash mechanisms are common in the market which utilise compliant pre- loads.
    [Show full text]
  • Electromagnetism What Is the Effect of the Number of Windings of Wire on the Strength of an Electromagnet?
    TEACHER’S GUIDE Electromagnetism What is the effect of the number of windings of wire on the strength of an electromagnet? GRADES 6–8 Physical Science INQUIRY-BASED Science Electromagnetism Physical Grade Level/ 6–8/Physical Science Content Lesson Summary In this lesson students learn how to make an electromagnet out of a battery, nail, and wire. The students explore and then explain how the number of turns of wire affects the strength of an electromagnet. Estimated Time 2, 45-minute class periods Materials D cell batteries, common nails (20D), speaker wire (18 gauge), compass, package of wire brad nails (1.0 mm x 12.7 mm or similar size), Investigation Plan, journal Secondary How Stuff Works: How Electromagnets Work Resources Jefferson Lab: What is an electromagnet? YouTube: Electromagnet - Explained YouTube: Electromagnets - How can electricity create a magnet? NGSS Connection MS-PS2-3 Ask questions about data to determine the factors that affect the strength of electric and magnetic forces. Learning Objectives • Students will frame a hypothesis to predict the strength of an electromagnet due to changes in the number of windings. • Students will collect and analyze data to determine how the number of windings affects the strength of an electromagnet. What is the effect of the number of windings of wire on the strength of an electromagnet? Electromagnetism is one of the four fundamental forces of the universe that we rely on in many ways throughout our day. Most home appliances contain electromagnets that power motors. Particle accelerators, like CERN’s Large Hadron Collider, use electromagnets to control the speed and direction of these speedy particles.
    [Show full text]
  • Electromagnetism
    EINE INITIATIVE DER UNIVERSITÄT BASEL UND DES KANTONS AARGAU Swiss Nanoscience Institute Electromagnetism Electricity and magnetism are two aspects of the same phenomenon: electromagnetism. A moving electric charge (in other words, an electric current) generates a magnetic field. Every electromagnet consists of a coil, which is nothing more than a tightly wound wire. Many electromagnets also have an iron core to make the magnetic field stronger. The more times the wire is wound around the coil, the stronger the magnetic field produced by the same current. Demonstration: Using electric current to create a magnetic field What you’ll need • a large sheet of paper on which to conduct the experiment • a sheet of stiff card or plexiglass • two batteries connected in series • a coil of copper wire • iron filings • crocodile clips (optional) • a small piece of iron (e.g. a screw) to place inside the coil (iron core) Instructions 1. Position the coil so that you can easily access the two ends of the wire and connect them to the battery. I used crocodile clips to attach them to the battery contacts, but you could also use wooden clothes pegs or electrical tape. 2. Connect the two batteries in series (+ - + - ). 3. Place the plexiglass or card over the coil. 4. When the electrical circuit is closed, slowly scatter the iron filings on top. What happens? The iron filings arrange themselves along the magnetic field lines. If you look closely, you can make out a pattern. Turn a screw into an electromagnet What you’ll need • a long iron screw or nail • two pieces of insulated copper wire measuring 15 and 30 cm • two three-pronged thumb tacks • a metal paperclip • a small wooden board • pins or paperclips • a 4.5 V battery Instructions Switch 1.
    [Show full text]
  • Roller Screws
    1213E_MSD_EXCO 1/11/06 10:06 AM Page 37 SIZEWISE Edited by Colleen Telling Sizing and applying ROLLER SCREWS Gary Shelton Roller screw shaft Principal Design Engineer Ground shaft Exlar Corp. Timing gear planetary Chanhassen, Minn. Roller screw nut roller screw How it works Roller screws convert ro- tary motion into linear mo- Roller screws’ tion just like acme and numerous ballscrews. Comparably contact points sized roller screws, however, vs. ballscrews’, have better efficiency than lengthen their acme screws and can carry lives and Spacer larger loads than ballscrews. washer increase load In addition, they can cycle Roller timing gear capacity and more often and turn signifi- stiffness. They Roller cantly faster than either, contain ground suiting them to precise, con- Retaining clip leadscrews for high- tinuous-duty applications. Roller journal precision applications Radiused flanks on the and come in tolerance rollers deliver point contact classes G1, G3, G4, and G5. like balls on a raceway, and only the radius is part of the profile. Therefore, a larger radius transversely and a precision- and additional contact points can ground spacer is inserted be- be packed into the available tween the front and back halves. space, thus lowering stress. In ad- The double nut is another alter- dition, the rolling contact be- native. As the name suggests, it tween components has low fric- uses two nuts preloaded against tion, yielding high efficiency. Be- each other on one screw. There is cause the rolling members are no sacrifice of life for its de- fixed relative to each other and creased backlash, but the double never touch adjacent rollers, nut costs more than standard sin- roller screws can turn at speeds gle-nut arrangements.
    [Show full text]
  • Light and Illumination
    ChapterChapter 3333 -- LightLight andand IlluminationIllumination AAA PowerPointPowerPointPowerPoint PresentationPresentationPresentation bybyby PaulPaulPaul E.E.E. Tippens,Tippens,Tippens, ProfessorProfessorProfessor ofofof PhysicsPhysicsPhysics SouthernSouthernSouthern PolytechnicPolytechnicPolytechnic StateStateState UniversityUniversityUniversity © 2007 Objectives:Objectives: AfterAfter completingcompleting thisthis module,module, youyou shouldshould bebe ableable to:to: •• DefineDefine lightlight,, discussdiscuss itsits properties,properties, andand givegive thethe rangerange ofof wavelengthswavelengths forfor visiblevisible spectrum.spectrum. •• ApplyApply thethe relationshiprelationship betweenbetween frequenciesfrequencies andand wavelengthswavelengths forfor opticaloptical waves.waves. •• DefineDefine andand applyapply thethe conceptsconcepts ofof luminousluminous fluxflux,, luminousluminous intensityintensity,, andand illuminationillumination.. •• SolveSolve problemsproblems similarsimilar toto thosethose presentedpresented inin thisthis module.module. AA BeginningBeginning DefinitionDefinition AllAll objectsobjects areare emittingemitting andand absorbingabsorbing EMEM radiaradia-- tiontion.. ConsiderConsider aa pokerpoker placedplaced inin aa fire.fire. AsAs heatingheating occurs,occurs, thethe 1 emittedemitted EMEM waveswaves havehave 2 higherhigher energyenergy andand 3 eventuallyeventually becomebecome visible.visible. 4 FirstFirst redred .. .. .. thenthen white.white. LightLightLight maymaymay bebebe defineddefineddefined
    [Show full text]
  • EMT UNIT 1 (Laws of Reflection and Refraction, Total Internal Reflection).Pdf
    Electromagnetic Theory II (EMT II); Online Unit 1. REFLECTION AND TRANSMISSION AT OBLIQUE INCIDENCE (Laws of Reflection and Refraction and Total Internal Reflection) (Introduction to Electrodynamics Chap 9) Instructor: Shah Haidar Khan University of Peshawar. Suppose an incident wave makes an angle θI with the normal to the xy-plane at z=0 (in medium 1) as shown in Figure 1. Suppose the wave splits into parts partially reflecting back in medium 1 and partially transmitting into medium 2 making angles θR and θT, respectively, with the normal. Figure 1. To understand the phenomenon at the boundary at z=0, we should apply the appropriate boundary conditions as discussed in the earlier lectures. Let us first write the equations of the waves in terms of electric and magnetic fields depending upon the wave vector κ and the frequency ω. MEDIUM 1: Where EI and BI is the instantaneous magnitudes of the electric and magnetic vector, respectively, of the incident wave. Other symbols have their usual meanings. For the reflected wave, Similarly, MEDIUM 2: Where ET and BT are the electric and magnetic instantaneous vectors of the transmitted part in medium 2. BOUNDARY CONDITIONS (at z=0) As the free charge on the surface is zero, the perpendicular component of the displacement vector is continuous across the surface. (DIꓕ + DRꓕ ) (In Medium 1) = DTꓕ (In Medium 2) Where Ds represent the perpendicular components of the displacement vector in both the media. Converting D to E, we get, ε1 EIꓕ + ε1 ERꓕ = ε2 ETꓕ ε1 ꓕ +ε1 ꓕ= ε2 ꓕ Since the equation is valid for all x and y at z=0, and the coefficients of the exponentials are constants, only the exponentials will determine any change that is occurring.
    [Show full text]
  • Surface Regularized Geometry Estimation from a Single Image
    SURGE: Surface Regularized Geometry Estimation from a Single Image Peng Wang1 Xiaohui Shen2 Bryan Russell2 Scott Cohen2 Brian Price2 Alan Yuille3 1University of California, Los Angeles 2Adobe Research 3Johns Hopkins University Abstract This paper introduces an approach to regularize 2.5D surface normal and depth predictions at each pixel given a single input image. The approach infers and reasons about the underlying 3D planar surfaces depicted in the image to snap predicted normals and depths to inferred planar surfaces, all while maintaining fine detail within objects. Our approach comprises two components: (i) a four- stream convolutional neural network (CNN) where depths, surface normals, and likelihoods of planar region and planar boundary are predicted at each pixel, followed by (ii) a dense conditional random field (DCRF) that integrates the four predictions such that the normals and depths are compatible with each other and regularized by the planar region and planar boundary information. The DCRF is formulated such that gradients can be passed to the surface normal and depth CNNs via backpropagation. In addition, we propose new planar-wise metrics to evaluate geometry consistency within planar surfaces, which are more tightly related to dependent 3D editing applications. We show that our regularization yields a 30% relative improvement in planar consistency on the NYU v2 dataset [24]. 1 Introduction Recent efforts to estimate the 2.5D layout of a depicted scene from a single image, such as per-pixel depths and surface normals, have yielded high-quality outputs respecting both the global scene layout and fine object detail [2, 6, 7, 29]. Upon closer inspection, however, the predicted depths and normals may fail to be consistent with the underlying surface geometry.
    [Show full text]
  • Chapter 16: Fourier Series
    Chapter 16: Fourier Series 16.1 Fourier Series Analysis: An Overview A periodic function can be represented by an infinite sum of sine and cosine functions that are harmonically related: Ϧ ͚ʚͨʛ Ɣ ͕1 ƍ ȕ ͕) cos ͢!*ͨ ƍ ͖) sin ͢!*ͨ Fourier Coefficients: are)Ͱͥ calculated from ͕1; ͕); ͖) ͚ʚͨʛ Fundamental Frequency: ͦ_ where multiples of this frequency are called !* Ɣ ; ͢! * harmonic frequencies Conditions that ensure that f(t) can be expressed as a convergent Fourier series: (Dirichlet’s conditions) 1. f(t) be single-values 2. f(t) have a finite number of discontinuities in the periodic interval 3. f(t) have a finite number of maxima and minima in the periodic interval 4. the integral /tͮ exists Ȅ/ |͚ʚͨʛ|ͨ͘; t These are sufficient conditions not necessary conditions; therefore if these conditions exist the functions can be expressed as a Fourier series. However if the conditions are not met the function may still be expressible as a Fourier series. 16.2 The Fourier Coefficients Defining the Fourier coefficients: /tͮ 1 ͕1 Ɣ ǹ ͚ʚͨʛͨ͘ ͎ /t /tͮ 2 ͕& Ɣ ǹ ͚ʚͨʛ cos ͟!*ͨ ͨ͘ ͎ /t /tͮ 2 ͖& Ɣ ǹ ͚ʚͨʛ sin ͟!*ͨ ͨ͘ ͎ / t Example 16.1 Find the Fourier series for the periodic waveform shown. Assessment problems 16.1 & 16.2 ECEN 2633 Spring 2011 Page 1 of 5 16.3 The Effects of Symmetry on the Fourier Coefficients Four types of symmetry used to simplify Fourier analysis 1. Even-function symmetry 2. Odd-function symmetry 3.
    [Show full text]
  • CS 468 (Spring 2013) — Discrete Differential Geometry 1 the Unit Normal Vector of a Surface. 2 Surface Area
    CS 468 (Spring 2013) | Discrete Differential Geometry Lecture 7 Student Notes: The Second Fundamental Form Lecturer: Adrian Butscher; Scribe: Soohark Chung 1 The unit normal vector of a surface. Figure 1: Normal vector of level set. • The normal line is a geometric feature. The normal direction is not (think of a non-orientable surfaces such as a mobius strip). If possible, you want to pick normal directions that are consistent globally. For example, for a manifold, you can pick normal directions pointing out. • Locally, you can find a normal direction using tangent vectors (though you can't extend this globally). • Normal vector of a parametrized surface: E1 × E2 If TpS = spanfE1;E2g then N := kE1 × E2k This is just the cross product of two tangent vectors normalized by it's length. Because you take the cross product of two vectors, it is orthogonal to the tangent plane. You can see that your choice of tangent vectors and their order determines the direction of the normal vector. • Normal vector of a level set: > [DFp] N := ? TpS kDFpk This is because the gradient at any point is perpendicular to the level set. This makes sense intuitively if you remember that the gradient is the "direction of the greatest increase" and that the value of the level set function stays constant along the surface. Of course, you also have to normalize it to be unit length. 2 Surface Area. • We want to be able to take the integral of the surface. One approach to the problem may be to inegrate a parametrized surface in the parameter domain.
    [Show full text]
  • Curl, Divergence and Laplacian
    Curl, Divergence and Laplacian What to know: 1. The definition of curl and it two properties, that is, theorem 1, and be able to predict qualitatively how the curl of a vector field behaves from a picture. 2. The definition of divergence and it two properties, that is, if div F~ 6= 0 then F~ can't be written as the curl of another field, and be able to tell a vector field of clearly nonzero,positive or negative divergence from the picture. 3. Know the definition of the Laplace operator 4. Know what kind of objects those operator take as input and what they give as output. The curl operator Let's look at two plots of vector fields: Figure 1: The vector field Figure 2: The vector field h−y; x; 0i: h1; 1; 0i We can observe that the second one looks like it is rotating around the z axis. We'd like to be able to predict this kind of behavior without having to look at a picture. We also promised to find a criterion that checks whether a vector field is conservative in R3. Both of those goals are accomplished using a tool called the curl operator, even though neither of those two properties is exactly obvious from the definition we'll give. Definition 1. Let F~ = hP; Q; Ri be a vector field in R3, where P , Q and R are continuously differentiable. We define the curl operator: @R @Q @P @R @Q @P curl F~ = − ~i + − ~j + − ~k: (1) @y @z @z @x @x @y Remarks: 1.
    [Show full text]