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kinetic

Energy of motion is usually called "kinetic energy."

503168Energy of motion is usually called "kinetic energy."

502167Available kinetic energy is possessed by a system of two or more bodies in virtue of the relative motion of its parts.

18888For a rigid body the kinetic energy will, in general, consist of three terms (AW1 2 +BW2 2 +CW3 2) in addition to the translational energy.

9969The kinetic energy of the molecules of these gases must contain two terms in addition to those representing translational energy.

7648Expenditure of Energy by Plants.The energy of the plant is, af we have seen, derived originally from the kinetic radiant energy 01 the sun.

5636A simple example of the transformation of kinetic energy into potential energy, and vice versa, is afforded by the pendulum.

4426These static and kinetic conditions succeed each other rapidly, and the result is to detach or throw off from the antenna semi-loops of electric force, which move outwards in all directions and are accompanied by expanding circular lines of magnetic force.

4244The agreement of the values obtained for the same quantity by different methods provides valuable confirmation of the truth of the molecular theory and of the validity of the methods of the kinetic theory of gases.

3626The hypothesis that the state was steady, so that interchanges arising from convection and collisions of the molecules produced no aggregate result, enabled him to interpret the new constants involved in this law of distribution, in terms of the temperature and its spacial differential coefficients, and thence to express the components of the kinetic stress at each point in the medium in terms of these quantities.

3523The kinetic energy of the liquid inside a surface S due to the velocity function 4' f i (s given by T=2p + (d) 2+ (t) dxdydz, pff f 75 4 dS (I) by Green's transformation, dv denoting an elementary step along the normal to the exterior of the surface; so that d4ldv = o over the surface makes T = o, and then (d4 2 d4) 2 'x) + (dy) + (= O, dd?

3336U, Kinetic energy of flow of fluid.

3226Tait and Dewar, as a consequence of the kinetic theory of the constitution of gaseous media.

3125The loss of energy could not be greater than this on the simple kinetic theory, unless there were some evolution of latent heat of co-aggregation, due to the work done by the mutual attractions of the co-aggregating molecules.

2922(to) Integrating over the base, to obtain one-third of the kinetic energy T, 3T = 2 pf '3 4R2(3x4-h4)dx/h 3 = pR2h4 / 1 35 V 3 (II) so that the effective k 2 of the liquid filling the trianglc is given by k 2 = T/Z p R 2 A = 2h2/45 = (radius of the inscribed circle) 2, (12) or two-fifths of the k 2 for the solid triangle.

2830(21) The comparison of this formula with experiment provides a striking confirmation of the truth of the kinetic theory but at the same time discloses the most formidable difficulty which the theory has so far had to encounter.

2327If mechanical work or kinetic energy is directly converted into heat by friction, reversal of the motion does not restore the energy so converted.

22213ZI /t = - (a - s) M'Q 2 sine cos ° - EQ sin() =[ - (a - (3)M'U+E]V (8) Now suppose the cylinder is free; the additional forces acting on the body are the components of kinetic reaction of the liquid - aM' (Ç_vR), - (3M' (-- E -FUR), - EC' dR, (9) so that its equations of motion are M (Ç - vR) _ - aM' (_vR) - (a - $) M'VR, (io) M (Ç+uR) = - OM' (dV+U R) - (a - ()M'UR - R, '(II) C dR = dR + (a - Q)M'UV+0V; (12) and putting as before M+aM'=ci, M+13M' = c2, C+EC'=C3, ci dU - c2VR=o, dV +(c1U+E)R=o, c 3 dR - (c 1 U+ - c 2 U)V =o; showing the modification of the equations of plane motion, due to the component E of the circulation.

2138The kinetic theory of gases attempts to give a mathematical account, in terms of the molecular structure of matter, of all the non-chemical and non-electrical properties of gases.

2023But supposing them determined for the motion of a body through a liquid, the kinetic energy T of the system, liquid and body, is expressible as a quadratic function of the components U, V, W, P, Q, R.

2024These theorems, which hold for the motion of a single rigid body, are true generally for a flexible system, such as considered here for a liquid, with one or more rigid bodies swimming in it; and they express the statement that the work done by an impulse is the product of the impulse and the arithmetic mean of the initial and final velocity; so that the kinetic energy is the work done by the impulse in starting the motion from rest.

1926This equation, which is mathematically deducible from the kinetic theory of gases, expresses the behaviour of gases, the phenomena of the critical state, and the behaviour of liquids; solids are not accounted for.

1821In this case the work of expansion, pdv, is expended in the first instance in producing kinetic energy of motion of parts of the gas.

1821The best estimates which we now possess of the sizes of molecules are provided by calculations based upon the kinetic theory of gases.

1821In this case the work of expansion, pdv, is expended in the first instance in producing kinetic energy of motion of parts of the gas.

1821Besides this most important contribution to the general fabric of dynamical science, we owe to Lagrange several minor theorems of great elegance, - among which may be mentioned his theorem that the kinetic energy imparted by given impulses to a material system under given constraints is a maximum.

1822There is probably but little transformation of one form of kinetic energy into another in the plant.

1829In the motion which can be solved by the elliptic function, the most general expression of the kinetic energy was shown by A.

1619Now the unstable movements of the needles are of a mechanically irreversible character; the energy expended in dissociating the members of a combination and placing them in unstable positions assumes the kinetic form when the needles turn over, and is ultimately frittered down into heat.

1621This energy is obtained especially by the chioroplastids, and part of it is at once devoted to the construction of carbohydrate material, being thus turned from the kinetic to the potential condition.

1622As a rule these equations are established immediately by determining the component acceleration of the fluid particle which is passing through (x, y, z) at the instant t of time considered, and saying that the reversed acceleration or kinetic reaction, combined with the impressed force per unit of mass and pressure-gradient, will according to d'Alembert's principle form a system in equilibrium.

1622Thus the estimation of kinetic energy is intimately affected by the choice of our base of measurement.

1522The determination of the series of configurations developing out of given initial conditions is not, however, the problem of the kinetic theory: the object of this theory is to explain the general properties of all gases in terms only of their molecular structure.

1522In the following table are given the values of the diameters of the molecules of six substances with which it is easy to experiment in the gaseous state, these values being calculated in different ways from formulae supplied by the kinetic theory.

1527In the following table are given the values of the diameters of the molecules of six substances with which it is easy to experiment in the gaseous state, these values being calculated in different ways from formulae supplied by the kinetic theory.

1527originally impinged on that at rest is now represented by the energy, kinetic and potential, of the small motions of the individual molecules.

1528Conversely, if the kinetic energy T is expressed as a quadratic function of x, x x3, y1, y2, y3, the components of momentum, the partial differential coefficient with respect to a momentum component will give the component of velocity to correspond.

1419If we consider any short length of the stream bounded by two imaginary cross-sections A and B on either side of the plug, unit mass of the fluid in passing A has work, p'v', done on it by the fluid behind and carries its energy, E'+ U', with it into the space AB, where U' is the kinetic energy of flow.

1318If we consider any short length of the stream bounded by two imaginary cross-sections A and B on either side of the plug, unit mass of the fluid in passing A has work, p'v', done on it by the fluid behind and carries its energy, E'+ U', with it into the space AB, where U' is the kinetic energy of flow.

1318In point of fact it is found that the properties which are most easily explained are those connected with the gaseous state; the explanation of these properties in terms of the molecular structure of matter is the aim of the " Kinetic Theory of Gases."

1320Instead of following the motion of each individual part of a material system, he showed that, if we determine its configuration by a sufficient number of variables, whose number is that of the degrees of freedom to move (there being as many equations as the system has degrees of freedom), the kinetic and potential energies of the system can be expressed in terms of these, and the differential equations of motion thence deduced by simple differentiation.

1219The Kinetic Theory of Gases.

1219b2' and this, by § 36, is also the ratio of the kinetic energy in the annular 4,1 interspace between the two cylinders to the kinetic energy of the liquid moving bodily inside r = b.

1121If a body whose mass is m grammes be moving with a velocity of v centimetres per second relative to the earth, the available kinetic energy possessed by the system is Zmv 2 ergs if m be small relative to the earth.

1016If a body whose mass is m grammes be moving with a velocity of v centimetres per second relative to the earth, the available kinetic energy possessed by the system is Zmv 2 ergs if m be small relative to the earth.

1016The remainder of this article is devoted to a brief statement of the methods and results of the kinetic theory.

1017The energy is less than that of an ideal gas by the term npc. If we imagine that the defect of volume c is due to the formation of molecular aggregates consisting of two or more single molecules, and if the kinetic energy of translation of any one of these aggregates is equal to that of one of the single molecules, it is clear that some energy must be lost in co-aggregating, but that the proportion lost will be different for different types of molecules and also for different types of co-aggregation.

818Wind turbines harness the power of the wind and convert its kinetic energy into electricity.

21The kinetic energy released by supernova explosions is more than enough to account for the Galactic cosmic rays up to 10 15 eV.

10He played a bouncy techno set from the hazy days of Kinetic alongside Storm.

10Topics include: chemical thermodynamics, kinetic molecular theory, chemical kinetics, and statistical thermodynamics.

10The increased kinetic motion of some receiving molecules should become vigorous enough to dislodge electrons.

10Kinetic Koffee has a few very well made coffees.

10Aluminum bats are more popular these days because of the fact that aluminum is more elastic than wood-this means that when the ball hits the bat, it retains more of its kinetic energy (i.e. it will go farther outward into the field).

10Wind power involves harnessing the kinetic energy in wind and converting it to electricity via a wind turbine.

10Blades attached to wind turbines collect the kinetic energy of wind, causing the blades to turn.

10The turning blades connect to a main drive shaft that spins a generator, converting the kinetic energy to electrical energy.

10Photovoltaic cells draw in heat from the sun, as a form of kinetic energy.

10Within each of these six renewable energy sources, scientists have discovered different methods to extract energy from kinetic motion, heat, sunlight and plant life.

10Kinetic Fountains is based in Asheville, North Carolina which is known for its stunning natural vistas.

10Games: Prince of Persia: Two Thrones, Peter Jackson's King Kong and the EyeToy: Kinetic games have all been released in the past few weeks.

10This is probably due to the fact that the younger athlete has a lower ratio of kinetic energy to body mass, which means the more immature the physical body, the lower the speed and power.

10It can be as simple as natural beauty or just natural kinetic energy; a particular mood or feeling can have a lot of influence on a design.

10Gemini children have a wiry, kinetic nature that keeps them moving constantly.

10Kinetic technology, which required no battery change and is powered by the movement of a person's body, was introduced in 1992.

10Featuring Kinetic chronograph, alarm chronograph, and analog-digital, these watches are powerful, yet stylish.

10These watches for men are bold and revolutionary, and they feature the most advanced Kinetic power.

10These include Kenetic Perpetual, Kinetic Auto Relay, and Kinetic Chronograph.

10Kinetic: Watches that have an internal rotating weight that winds the watch as you move your wrist.

10Rotor: The component of a kinetic watch that winds the mainspring as the wearer moves.

10Seiko also employs kinetic technology in which a tiny electric generator in the watch is powered by wrist movement, eliminating the need for any sort of conventional battery.

10The newest and most impressive addition to the Premier line is the Kinetic Perpetual, which makes use of Seiko's new kinetic power method.

10The Kinetic Perpetual boasts a calendar, which is guaranteed accurate until the year 2100, hence the name "Perpetual."

10The Arctura line showcases the heart of the kinetic movement, offering three unique models.

10The Kinetic, the Kinetic Chronograph, and the Kinetic Auto Relay all offer sleek, conventional designs with the lasting satisfaction that your timepiece will keep time for years to come.

10The Kinetic Chronograph, like the name implies, offers choreographing technology, which will chronograph to 1/5 of a second for up to 45 minutes.

10The Kinetic Auto Relay, like the Kinetic Perpetual, will power down after 72 hours of non-use.

10A lot of Seiko's new watches utilize "kinetic" technology, meaning that the watch contains a tiny electric motor that is powered by the wearer's natural wrist movements.

10The Kinetic Perpetual, the star of the Premier line-up, features the kinetic technology that I covered earlier in this article.

10Seiko's Arctura line is the hotspot for the company's new kinetic technology.

10With three distinct models, the Arctura line showcases what kinetic is really capable of.

10The Kinetic technology also features a "shut-down" feature.

10Seiko went on to acquire and launch additional brands, like Pulsar, and to introduce innovative products like the first TV watch and kinetic watches that don't require batteries.

10The Sportura line features rugged, stainless steel men's sports watches made with kinetic and alarm chronograph technologies as well as analog-digital styles.

10Coutura watches boast kinetic technology, which will never need a battery change, as well as chronograph watches.

10These attractive timepieces are available with convenient kinetic technology and chronograph styles as well.

10Sportura: This men's watch has a kinetic chronograph and alarm chronograph.

10Arctura: The Arctura is a slightly higher end kinetic power watch.

10Built to function forever and made to last with kinetic energy powered by your body's natural movements.

10They are referring to the kinetic chain, which is the sequence of a given athletic movement.

10Defensive upgrades include a few hundred kinetic energy turrets and a few prized nukes.

10In plane motion the kinetic energy per unit length parallel to Oz T 2p J J [(d4)) 2+ (d dy (P)1dxdy=lpfl[ a) 2+ (=zp 4d ds=zp f, ydvds.

00We shall show that if we sum these up for a whole wave the potential energy is equal to the kinetic energy.

00The kinetic energy per cubic centimetre is 2 pu t, where is the density and u is the velocity of disturbance due to the passage of the wave.

00If r is of the order of A, n is of the order of y; and the kinetic energy of the radial motion is of the same order as that of the longitudinal motion.

00During the quarter swing ending with greatest nodal pressure, the kinetic energy is changed to potential energy manifested in the increase of pressure.

00This becomes again kinetic in the second quarter swing, then in the third quarter it is changed to potential energy again, but now manifested in the decrease of pressure.

00In the last quarter it is again turned to the kinetic form.

00There will be more kinetic energy formed in the return journey and the vibration tends to grow.

00But if the heat is given at the instant of greatest rarefaction, the increase of pressure lessens the difference from the undisturbed pressure, and lessens the potential energy, so that during the return less kinetic energy is formed and the vibration tends to die away.

00Let E be the effective elasticity of the aether; then E = pc t, where p is its density, and c the velocity of light which is 3 X 10 10 cm./sec. If = A cos" (t - x/c) is the linear vibration, the stress is E dE/dx; and the total energy, which is twice the kinetic energy Zp(d/dt) 2 dx, is 2pn2A2 per cm., which is thus equal to 1.8 ergs as above.

00If we rest on the synthesis here described, the energy of the matter, even the thermal part, appears largely as potential energy of strain in the aether which interacts with the kinetic energy associated with disturbances involving finite velocity of matter.

00When the atoms are in motion these strain-forms produce straining and unstraining in the aether as they pass across it, which in its motional or kinetic aspect constitutes the resulting magnetic field; as the strains are slight the coefficient of ultimate inertia here involved must be great.

00After a certain discount for friction and the recoil of the gun, the net work realized by the powder-gas as the shot advances AM is represented by the area Acpm, and this is equated to the kinetic energy e of the shot, in foot-tons, (I) e d2 I + p, a in which the factor 4(k 2 /d 2)tan 2 S represents the fraction due to the rotation of the shot, of diameter d and axial radius of gyration k, and S represents the angle of the rifling; this factor may be ignored in the subsequent calculations as small, less than I %.

00The importance of a study of the changes of the vis viva depending on squares of velocities, or what is now called the "kinetic energy" of a system, was recognized in Newton's time, especially by Leibnitz; and it was perceived (at any rate for special cases) that an increase in this quantity in the course of any motion of the system was otherwise expressible by what we now call the "work" done by the forces.

00The energy of a system is the measure of its capacity for doing work, on the assumption of suitable connexions with other systems. When the motion of a body is checked by a spring, its kinetic energy being destroyed, the spring, if perfectly elastic, is capable of restoring the motion; but if it is checked by friction no such restoration can be immediately effected.

00On certain assumptions required for the extension of the methods of the kinetic theory of gases to liquids, L.

00We can calculate, by the help of the kinetic theory and the theory of chances, the frequency with which the necessary conjunctions of ions will occur, and show that the general law will be that the coagulative powers should be in the ratios of 1: x: x 2.

004, which, according to the kinetic theory, is an indication that an important fraction of the energy absorbed is devoted to rotation or vibration.

00It is much more probable that heat is really the kinetic energy of motion of the molecules, and is passed on from one to another by collisions.

00The high conductivity of metals is then explained by the small mass and high velocity of diffusion of these electric atoms. Assuming the kinetic energy of an electric atom at any temperature to be equal to that of a gaseous molecule, its velocity, on Sir J.

00On the kinetic theory the molecules of a gas are relatively far apart and there is nothing analogous to friction between two adjacent layers A and B moving with different velocities.

00This potential energy becomes kinetic when the slag is brought into contact with lime in the presence of water, and causes the formation of a true hydraulic silicate of lime.

00Thus The Direct Experimental Evidence Is Somewhat Meagre And Conflicting, But The Question Of The Relation Of The Specific Heats Of Gases Is One Of Great Interest In Connexion With The Kinetic Theory And The Constitution Of The Molecule.

00According To The Elementary Kinetic Theory Of An Ideal Gas, The Molecules Of Which Are So Small And So Far Apart That Their Mutual Actions May Be Neglected, The Kinetic Energy Of Translation Of The Molecules Is Proportional To The Absolute Temperature, And Is Equal To 3/2 Of Pv, The Product Of The Pressure And The Volume, Per Unit Mass.

00If The Molecules Are Supposed To Be Like Smooth, Hard, Elastic Spheres, Incapable Of Receiving Any Other Kind Of Energy Except That Of Translation, The Specific Heat At Constant Volume Would Be The Increase Per Degree Of The Kinetic Energy Namely 3Pv/20=3R/2, That At Constant Pressure Would Be 5R/2, And The Ratio Of The Specific Heats Would Be 5/3 Or 1.666.

00In 1879 Maxwell Considered It One Of The Greatest Difficulties Which The Kinetic Theory Had Yet Encountered, That In Spite Of The Many Other Degrees Of Freedom Of Vibration Revealed By The Spectroscope, The Experimental Value Of The Ratio S/S Was 1.40 For So Many Gases, Instead Of Being Less Than 4/3.

00When Bosanquet says that in " Heat is a mode of motion " there is no reference to individual objects, but " a pure hypothetical form which absolutely neglects the existence of objects," he falls far short of expressing the nature of this scientific judgment, for in his Theory of Heat Clerk Maxwell describes it as " believing heat as it exists in a hot body to be in the form of kinetic energy."

00If steam or vapour is " wire-drawn " or expanded through a porous plug or throttling aperture without external loss or gain of heat, the total heat (E+pv) remains constant (Thermodynamics, § I I), provided that the experiment is arranged so that the kinetic energy of flow is the same on either side of the throttle.

00The mass-system is then said to possess kinetic symmetry about 0.

00Young in connection with the kinetic theory of the tides, where the same point arises.

00The product 4muf is called the kinetic energy of the particle, and the equation.

00(21) is therefore equivalent to the statement that the increment of the kinetic energy is equal to the work done on the particle.

00which asserts that when no extraneous forces act the sum of the kinetic and potential energies is constant.

00be to increase the sum of the kinetic and potential energies by an amount equal to the work done by them.

00If we assume that there is no loss of apparent kinetic energy we have also miuii +miuf2 = miui2 +mfuzi.

00It follows from the formula 15 (10) for the internal kinetic energy of a system of particles that as a result of the impact this energy is diminished by the amount i m1mi 2(1 _ei)m+m(ui_uf)1.

00The unit of work on the same principles is ML2T2, and itis to be noticed that this is identical with the unit of kinetic energy.

00Next consider the kinetic energy of the system.

00the total kinetic energy is equal to the kinetic energy of the whole mass supposed concentrated at G and moving with this point, together with the kinetic energy of the motion relative to G.

00The latter may be called the internal kinetic energy of the system.

00which expresses the internal kinetic energy in terms of the relative velocities of the several pairs of particles.

00Also by (10) the internal kinetic energy is - m,m~

00mif-mi The increase of the kinetic energy of the system in any interval of time will of course be equal to the total work done by all the forces acting on the particles.

00If T denote the kinetic energy, we may say then that the sum T + V is in any interval of time increased by an amount equal to the work done by the extraneous forces.

00The increase of the kinetic energy of a rigid body in any interval of time is equal to the work done by the extraneous forces acting on the body.

00(13) The left-hand side is the kinetic energy of the whole mass, supposed concentrated at G and moving with this point, together with the kinetic energy of the motion relative to G (15); and the right-hand member represents the integral work done by the extraneous forces in the successive infinitesimal displacements into which the motion may be resolved.

00the kinetic energy is 3/4MK262+

00If q be any variable co-ordinate defining the position or (in the case of a system of bodies) the configuration, the velocity of each particle at any instant will be proportional to 4, and the total kinetic energy may be expressed in the form 1/8A42, where A is in general a function of q The special case where both cones are right circular and a is constant is important ~n astronomy and also in mechanism (theory of bevel wheels).

00If m be the mass of a particle at P, and PN the perpendicular to the instantaneous axis, the kinetic energy T is given by 2T=2~{m(w.

00In this case the kinetic energy is given by 2T = M0 (u1 +v2+w1) +AP2 +Bq2 +Cr2 2Fqr 2Grp 2Hpq, (13) where M0 is the mass, and A, B, C, F, G, H are the moments and products of inertia with respect to the mass-centre; cf.

00Hence the change of kinetic energy is TT=~.1/8(u+u) +n.1/8(v+v)+1.1/8(w+w),

00We are thus led to the following statement: the change of kinetic energy due to any system of impulsive forces is equal to the sum of the products of the several forces into the semisum of the initial and final velocities of their respective points of application, resolved in the directions of the forces.

0077 the kinetic energy generated is ~M (ic2H- Cq2)cuf, if C be the instantaneous centre; this is seen to be equal to ~F.

00The kinetic energy T of the motion relative to 0 will be constant.

00Motion of a Solid of Revolution.In the case of a solid of revolution, or (more generally) whenever there is kinetic syminetry about an asks through the mass-centre, or through a fixec point 0, a number of interesting problems can be treated almost directly from first principles.

00If the direction of the axis of kinetic symmetry be specified by means of the angular co-ordinates 0, ~

00kinetic energy is given by 2T=A(O2+sinO ~2)+Cnh.

00The former is, in fact, equal to 2T, and the latter to ~2, where T is the kinetic energy an.d r the resultant angular momentum.

00If OA, OB, OC be principal axes of inertia of a solid, and if A, B, C denote the corresponding moments of inertia, the kinetic energy is given by 2TA(~ sin 4,sin 0 cos 44~)2+B Ce cos 4,+sin0 sin$)i +C (~+cos0~)2.

00This equation expresses that the kinetic energy is increasing at a rate equal to that at which work is being done by the forces.

00To apply the equations (11) to the case of the top we start with the expression (15) of 22 for the kinetic energy, the simplified form (i) of 20 being for the present purpose inadmissible, since it is essential that the generalized co-ordinates employed should be competent to specify the position of every particle.

00Connecting the experimental study of the physical and chemical properties is the immense theoretical edifice termed the kinetic theory of gases.

00But no one can tell whether the study of physiological phenomena in general, and of nervous phenomena in particular, will not reveal to us, besides the vis viva or kinetic energy of which Leibnitz spoke, and the potential energy which was a later and necessary adjunct, some new kind of energy which may differ from the other two by rebelling against calculation" (Bergson, Time and Free Will, Eng.

00203) show that chemical action is to be referred to the latter of these vectors, but whether Fresnel's or Neumann's hypothesis be correct is only to be decided when we know if it be the mean kinetic energy or the mean potential energy that determines chemical action.

00Ann., 1875), who regarded electricity as consisting of atoms much smaller than those of matter, and supposed that heat was the kinetic energy of these electric atoms. If we suppose that an electric current in a metal is a flow of negative electric atoms in one direction, the positive electricity associated with the far heavier material atoms remaining practically stationary, and if the atomic heat of electricity is of the same order as that of an equivalent quantity of hydrogen or any other element, the heat carried per ampere-second at o C., namely P, would be of the order of 030 of a joule, which would be ample to account for all the observed effects on the convection theory.

00Coulomb pointed out long ago that the resistance of a body to be set in motion was in many cases much greater than the resistance which it offered to continued motion; and since his time writers have always distinguished the "friction of rest," or static friction, from the "friction of motion," or kinetic friction.

00These experiments distinctly point to the conclusion, although without absolutely proving it, that in such cases the coefficient of kinetic friction gradually increases as the velocity becomes extremely small, and passes without discontinuity into that of static friction.

00accelerated from rest, also acquires kinetic energy and so its inertial mass must increase as speed increases.

00G-actin was polymerized into F-actin in a similar kinetic process to rabbit muscle actin was polymerized into F-actin in a similar kinetic process to rabbit muscle actin.

00Kinetic methods which measure the clearances (removal) of urea and creatinine are now the gold standard for the assessment of dialysis adequacy.

00Bayesian inference for stochastic kinetic models using a diffusion approximation.

00Research areas include bioenergetics, molecular biology, fermentation, protein biochemistry, kinetic and paramagnetic spectroscopy and X-ray crystallography.

00Chen, O. Delumeau and M. Yudkin) we are measuring a variety of kinetic and equilibrium constants for RsbT and RsbU.

00dispersion relation for the arbitrary velocity distribution in a fully kinetic limit is obtained.

00Viscid silk also needs to absorb the kinetic energy of the fly, corresponding to a high value.

00Hamiltonian matrix is then calculated using the discrete Fast Fourier Transform method to compute the kinetic energy part of the operator.

00Hence one can generally safely neglect kinetic inductance for normal electronics.

00inelastic collisions are those in which kinetic energy is not conserved.

00instantaneous snapshot during the interaction of incoming wake with gas turbine blade showing dynamically adapted mesh & turbulence kinetic energy distribution.

00The kinetic transport coeffs. are computed from explicit collision integrals and compared favorably with detailed simulations.

00A constellation of space-based kinetic interceptors could not be deployed for many years, although small numbers of prototypes could possibly be deployed earlier.

00Waves and instabilities in fully ionized (and magnetized) fluid and kinetic plasmas will also be addressed.

00Kinetic Whitney falls in with some former jocks who have kryptonite tattoes that give them the power to walk through the walls.

00This means that you already have 108 thousand joules of kinetic energy for every kg.

00kinetic energy of the air current, cooling the air which then descends.

00kinetic sculpture given to the house by the artist George Rickey.

00kinetic modeling.

00kinetic theory of gases.

00kinetic equations to the level of fluid mechanics.

00kinetic parameters like K m.

00A high temperature from a match or spark etc., gives the reactant molecules enough kinetic energy to overcome the activation energy * .

00There is an incredibly kinetic dynamic to act for him.

00If enough individuals turn kinetic, it starts accelerating into a collective form.

00Tony comments that, " although the structure was fastened, as the viewer moved around the form it became kinetic.

00kinetic energy of the fly, corresponding to a high value.

00Viscid silk also needs to absorb the kinetic energy of the fly, corresponding to a high value.

00Air from the atmosphere enters the eye of the first impeller it then acquires kinetic energy from the rotating impellers.

00Mecca simply wanted what they eventually got - pure raw, kinetic energy dispersed under a geometric ceiling that resembled an inverted space station.

00In both static and kinetic perimetry, the effective visual field enlarged during the training.

00Kinetic studies on the nanosecond timescale are also possible using a laser flash photolysis instrument.

00In both cases, we need extensive experimental studies seeking to identify all long-lived polymorphs in order to understand the kinetic factors involved.

00This should ensure that the data-mining analysis could find the most effective correlation between the observed polymorphs and the predicted thermodynamic and kinetic properties.

00Hence, we need to rationalize the kinetic factors that can lead to the observation of metastable polymorphs.

00Kinetic an crystallographic analysis of the key active site acid/base arginine in a soluble fumarate reductase.

00Identification of the active site acid/base catalyst in a bacterial fumarate reductase: a kinetic and crystallographic study.

00The high kinetic energies are needed to overcome the repulsion of the two positive nuclei.

00It slows down, losing kinetic energy as its potential energy, of electrical repulsion, increases in compensation.

00kinetic sculptures by Jean Tinguely are on display to 24th September.

00These kinetic differences were confirmed by short-term in vitro culture both in fetal calf serum and in AS.

00viscid silk also needs to absorb the kinetic energy of the fly, corresponding to a high value.

00instantaneous snapshot during the interaction of incoming wake with gas turbine blade showing dynamically adapted mesh & turbulence kinetic energy distribution.

00Q: Is bug splat only for kinetic weapons?

00He played a bouncy techno set from the hazy days of Kinetic alongside Storm.

00Topics include: chemical thermodynamics, kinetic molecular theory, chemical kinetics, and statistical thermodynamics.

00The increased kinetic motion of some receiving molecules should become vigorous enough to dislodge electrons.

00For the best solution a prize was offered by the philosophical faculty of the University, and this he succeeded in winning with the paper which was published in 1880 on the "Kinetic Energy of Electricity in Motion."

00A simple example of the transformation of kinetic energy into potential energy, and vice versa, is afforded by the pendulum.

00When passing through its position of equilibrium, since gravity can do no more work upon it without changing its fixed point of support, all the energy of oscillation is kinetic. At intermediate positions the energy is partly kinetic and partly potential.

00Available kinetic energy is possessed by a system of two or more bodies in virtue of the relative motion of its parts.

00Thus the estimation of kinetic energy is intimately affected by the choice of our base of measurement.

00When the stresses acting between the parts of a system depend only on the relative positions of those parts, the sum of the kinetic energy and potential energy of the system is always the same, provided the system be not acted upon by anything outside it.

00In some cases, as when heat is converted into the kinetic energy of moving machinery or the potential energy of raised weights, there is an ascent of energy from the less available form of heat to the more available form of mechanical energy, but in all cases this is accompanied by the transfer of other heat from a body at a high temperature to one at a lower temperature, thus losing availability to an extent that more than compensates for the rise.

00These static and kinetic conditions succeed each other rapidly, and the result is to detach or throw off from the antenna semi-loops of electric force, which move outwards in all directions and are accompanied by expanding circular lines of magnetic force.

00This energy is obtained especially by the chioroplastids, and part of it is at once devoted to the construction of carbohydrate material, being thus turned from the kinetic to the potential condition.

00Thus even ir these constructive processes there occurs a constant pas,age of energy backwards and forwards from the kinetic to the potential condition and vice versa.

00There is probably but little transformation of one form of kinetic energy into another in the plant.

00Expenditure of Energy by Plants.The energy of the plant is, af we have seen, derived originally from the kinetic radiant energy 01 the sun.

00These expressions indicate what frequent changes in the power are required as the train pursues its journey up and down gradients, against wind resistance, j ournal friction and perhaps the resistance of a badly laid track; and show how both the potential energy and kinetic energy of the train are continually changing: the first from a change in vertical position due to the gradients, the second from changes in speed.

00One of his greatest investigations bore on the " Kinetic Theory of Gases."

00Between 1886 and 1892 he published a series of papers on the foundations of the kinetic theory of gases, the fourth of which contained what was, according to Lord Kelvin, the first proof ever given of the Waterstdn-Maxwell theorem of the average equal partition of energy in a mixture of two different gases; and about the same time he carried out investigations into impact and its duration.

00This equation, which is mathematically deducible from the kinetic theory of gases, expresses the behaviour of gases, the phenomena of the critical state, and the behaviour of liquids; solids are not accounted for.

00By considerations based on the kinetic theory of gases (see Molecule) it may be shown that when no energy is utilized in separating the atoms of a molecule, this ratio is 5/3= 1.67.

00Now the unstable movements of the needles are of a mechanically irreversible character; the energy expended in dissociating the members of a combination and placing them in unstable positions assumes the kinetic form when the needles turn over, and is ultimately frittered down into heat.

00Instead of following the motion of each individual part of a material system, he showed that, if we determine its configuration by a sufficient number of variables, whose number is that of the degrees of freedom to move (there being as many equations as the system has degrees of freedom), the kinetic and potential energies of the system can be expressed in terms of these, and the differential equations of motion thence deduced by simple differentiation.

00Besides this most important contribution to the general fabric of dynamical science, we owe to Lagrange several minor theorems of great elegance, - among which may be mentioned his theorem that the kinetic energy imparted by given impulses to a material system under given constraints is a maximum.

00As a rule these equations are established immediately by determining the component acceleration of the fluid particle which is passing through (x, y, z) at the instant t of time considered, and saying that the reversed acceleration or kinetic reaction, combined with the impressed force per unit of mass and pressure-gradient, will according to d'Alembert's principle form a system in equilibrium.

00b2' and this, by § 36, is also the ratio of the kinetic energy in the annular 4,1 interspace between the two cylinders to the kinetic energy of the liquid moving bodily inside r = b.

00With liquid of density p, this gives rise to a kinetic reaction to acceleration dU/dt, given by 7rp b 2 a 2 b l b d J = a 2 +b2 M' dU, if M' denotes the mass of liquid displaced by unit length of the cylinder r =b.

00Round the cylinder r=a held fixed in the U current the liquid streams past with velocity q' =2U sin 0+m/a; (2) and the loss of head due to this increase of velocity from U to q' is q' 2 -U 2 - (2U sin e to space filled with liquid, and at rest at infinity, the cylinder will experience components of force per unit length (i.) -27rpmV, 27rpmU, due to the vortex motion; 2 dU 2dV (ii.) -71-pa 2 w,, -7rpa dt, due to the kinetic reaction of the liquid; (iii.) o, -7r(a-p)a 2 g, due to gravity, taking Oy vertically upward, and denoting the density of the cylinder by a; so that the equations of motion are 71-0-a 2 - di r = - 7pa2- -- 22rpmV, (4) aa 2 - = -7rpa 2 dV +27rpmV - 7r(cr - p) a2g, (5) 7r or, putting m = a 2 w, so that the vortex velocity is due to an angular velocity w at a radius a, (o+p)dU/dt+2pwV =o, (6) (a+ p) dV /dt - 2 pwU + (v - p)g = o.

00The kinetic energy of the liquid inside a surface S due to the velocity function 4' f i (s given by T=2p + (d) 2+ (t) dxdydz, pff f 75 4 dS (I) by Green's transformation, dv denoting an elementary step along the normal to the exterior of the surface; so that d4ldv = o over the surface makes T = o, and then (d4 2 d4) 2 'x) + (dy) + (= O, dd?

00To find the kinetic energy of such motion in a multiply connected space, the channels must be supposed barred, and the space made acyclic by a membrane, moving with the velocity of the liquid; and then if k denotes the cyclic constant of 0 in any circuit, or the value by which 4) has increased in completing the circuit, the values of 0 on the two sides of the membrane are taken as differing by k, so that the integral over the membrane dS= k f ?

00d ddS, and this term is to be added to the terms in (I) to obtain the additional part in the kinetic energy; the continuity shows that the integral is independent of the shape of the barrier membrane, and its position.

00In plane motion the kinetic energy per unit length parallel to Oz T 2p J J [(d4)) 2+ (d dy (P)1dxdy=lpfl[ a) 2+ (=zp 4d ds=zp f, ydvds.

00(to) Integrating over the base, to obtain one-third of the kinetic energy T, 3T = 2 pf '3 4R2(3x4-h4)dx/h 3 = pR2h4 / 1 35 V 3 (II) so that the effective k 2 of the liquid filling the trianglc is given by k 2 = T/Z p R 2 A = 2h2/45 = (radius of the inscribed circle) 2, (12) or two-fifths of the k 2 for the solid triangle.

00But supposing them determined for the motion of a body through a liquid, the kinetic energy T of the system, liquid and body, is expressible as a quadratic function of the components U, V, W, P, Q, R.

00Conversely, if the kinetic energy T is expressed as a quadratic function of x, x x3, y1, y2, y3, the components of momentum, the partial differential coefficient with respect to a momentum component will give the component of velocity to correspond.

00These theorems, which hold for the motion of a single rigid body, are true generally for a flexible system, such as considered here for a liquid, with one or more rigid bodies swimming in it; and they express the statement that the work done by an impulse is the product of the impulse and the arithmetic mean of the initial and final velocity; so that the kinetic energy is the work done by the impulse in starting the motion from rest.

00In the motion which can be solved by the elliptic function, the most general expression of the kinetic energy was shown by A.

00ZI /t = - (a - s) M'Q 2 sine cos Ã‚° - EQ sin() =[ - (a - (3)M'U+E]V (8) Now suppose the cylinder is free; the additional forces acting on the body are the components of kinetic reaction of the liquid - aM' (Ã‡_vR), - (3M' (-- E -FUR), - EC' dR, (9) so that its equations of motion are M (Ã‡ - vR) _ - aM' (_vR) - (a - $) M'VR, (io) M (Ã‡+uR) = - OM' (dV+U R) - (a - ()M'UR - R, '(II) C dR = dR + (a - Q)M'UV+0V; (12) and putting as before M+aM'=ci, M+13M' = c2, C+EC'=C3, ci dU - c2VR=o, dV +(c1U+E)R=o, c 3 dR - (c 1 U+ - c 2 U)V =o; showing the modification of the equations of plane motion, due to the component E of the circulation.

00The assumption usually made is that the total kinetic energy of the molecules, including possible energy of rotation or vibration if the molecules consist of more than one atom, is proportional to the energy of translation in the case of an ideal gas.

00The energy is less than that of an ideal gas by the term npc. If we imagine that the defect of volume c is due to the formation of molecular aggregates consisting of two or more single molecules, and if the kinetic energy of translation of any one of these aggregates is equal to that of one of the single molecules, it is clear that some energy must be lost in co-aggregating, but that the proportion lost will be different for different types of molecules and also for different types of co-aggregation.

00The loss of energy could not be greater than this on the simple kinetic theory, unless there were some evolution of latent heat of co-aggregation, due to the work done by the mutual attractions of the co-aggregating molecules.

00If mechanical work or kinetic energy is directly converted into heat by friction, reversal of the motion does not restore the energy so converted.

00If this could be co-ordinated and utilized without dissipation, the gas might conceivably be restored to its initial state; but in practice violent local differences of pressure and temperature are produced, the kinetic energy is rapidly converted into heat by viscous eddy friction, and residual differences of temperature are equalized by diffusion throughout the mass.

00As the section of the tube varies, the change of kinetic energy of flow, dU, is represented by The flow in this case is reversible, and the state of the fluid is the same at points where the section of the tube is the same.

00U, Kinetic energy of flow of fluid.

00Tait and Dewar, as a consequence of the kinetic theory of the constitution of gaseous media.

00The hypothesis that the state was steady, so that interchanges arising from convection and collisions of the molecules produced no aggregate result, enabled him to interpret the new constants involved in this law of distribution, in terms of the temperature and its spacial differential coefficients, and thence to express the components of the kinetic stress at each point in the medium in terms of these quantities.

00In point of fact it is found that the properties which are most easily explained are those connected with the gaseous state; the explanation of these properties in terms of the molecular structure of matter is the aim of the " Kinetic Theory of Gases."

00The best estimates which we now possess of the sizes of molecules are provided by calculations based upon the kinetic theory of gases.

00The agreement of the values obtained for the same quantity by different methods provides valuable confirmation of the truth of the molecular theory and of the validity of the methods of the kinetic theory of gases.

00The kinetic energy with which the moving mass.

00originally impinged on that at rest is now represented by the energy, kinetic and potential, of the small motions of the individual molecules.

00It is known, however, that when two bodies impinge, the kinetic energy which appears to be lost from the mass-motion of the bodies is in reality transformed into heat-energy.

00The kinetic theory of gases attempts to give a mathematical account, in terms of the molecular structure of matter, of all the non-chemical and non-electrical properties of gases.

00The remainder of this article is devoted to a brief statement of the methods and results of the kinetic theory.

00The Kinetic Theory of Gases.

00The determination of the series of configurations developing out of given initial conditions is not, however, the problem of the kinetic theory: the object of this theory is to explain the general properties of all gases in terms only of their molecular structure.

00In this expression the first line may be supposed to represent the energy (or part of the energy) of s similar molecules of a kind which we shall call the first kind, the terms 2 (mu 2 +mv 2 +mw 2) being the kinetic energy of translation, and the remaining terms arising from energy of rotation or of internal motion, or from the energy, kinetic and potential, of small vibrations.

00For instance, if the system is composed of a gas and a solid boundary, some of the terms in expression (2) may be supposed to represent the kinetic energy of the molecules of the boundary, so that equations (7) show that in the normal state the gas has the same temperature as the boundary.

00It will at once be apparent that the kinetic theory of matter enables us to place the second law of thermodynamics upon a purely dynamical basis.

00Thus the " Brownian movements " provide visual demonstration of the reality of the heat-motion postulated by the kinetic theory.

00(21) The comparison of this formula with experiment provides a striking confirmation of the truth of the kinetic theory but at the same time discloses the most formidable difficulty which the theory has so far had to encounter.

00The kinetic energy of the molecules of these gases must contain two terms in addition to those representing translational energy.

00For a rigid body the kinetic energy will, in general, consist of three terms (AW1 2 +BW2 2 +CW3 2) in addition to the translational energy.

00The energy in a train of waves carried forward with the waves is partly strain or potential energy due to change of volume of the air, partly kinetic energy due to the motion of the air as the waves pass.

00We shall show that if we sum these up for a whole wave the potential energy is equal to the kinetic energy.

00The kinetic energy per cubic centimetre is 2 pu t, where is the density and u is the velocity of disturbance due to the passage of the wave.

00But v/V =u/U from equation (2) and w =Eu/U from equation (3) Then 2wv/V = ZEu 2 /U 2 = 2 pu t from equation (6) Then in the whole wave the potential energy equals the kinetic energy and the total energy in a complete wave in a column 1 sq.

00If r is of the order of A, n is of the order of y; and the kinetic energy of the radial motion is of the same order as that of the longitudinal motion.

00During the quarter swing ending with greatest nodal pressure, the kinetic energy is changed to potential energy manifested in the increase of pressure.

00This becomes again kinetic in the second quarter swing, then in the third quarter it is changed to potential energy again, but now manifested in the decrease of pressure.

00In the last quarter it is again turned to the kinetic form.

00There will be more kinetic energy formed in the return journey and the vibration tends to grow.

00But if the heat is given at the instant of greatest rarefaction, the increase of pressure lessens the difference from the undisturbed pressure, and lessens the potential energy, so that during the return less kinetic energy is formed and the vibration tends to die away.

00Let E be the effective elasticity of the aether; then E = pc t, where p is its density, and c the velocity of light which is 3 X 10 10 cm./sec. If = A cos" (t - x/c) is the linear vibration, the stress is E dE/dx; and the total energy, which is twice the kinetic energy Zp(d/dt) 2 dx, is 2pn2A2 per cm., which is thus equal to 1.8 ergs as above.

00If we rest on the synthesis here described, the energy of the matter, even the thermal part, appears largely as potential energy of strain in the aether which interacts with the kinetic energy associated with disturbances involving finite velocity of matter.

00It may, however, be maintained that an ultimate analysis would go deeper, and resolve all phenomena of elastic resilience into consequences of the kinetic stability of steady motional states, so that only motions, but not strains, would remain.

00When the atoms are in motion these strain-forms produce straining and unstraining in the aether as they pass across it, which in its motional or kinetic aspect constitutes the resulting magnetic field; as the strains are slight the coefficient of ultimate inertia here involved must be great.

00in the time At, during which the velocity falls from v+2Av to v-2Av, we have (12) RAs = loss of kinetic energy in foot-pounds =w(v+ZOv) 2 /g - w(v - ZOv) 2 /g=wvAv/g, so that (13) As =wvAv/nd 2 pg =CAS, where (14) AS = vAv/g p = vAT, and AS is the advance in feet of a shot for which C =1, while the velocity falls Av in passing through the average velocity v.

00After a certain discount for friction and the recoil of the gun, the net work realized by the powder-gas as the shot advances AM is represented by the area Acpm, and this is equated to the kinetic energy e of the shot, in foot-tons, (I) e d2 I + p, a in which the factor 4(k 2 /d 2)tan 2 S represents the fraction due to the rotation of the shot, of diameter d and axial radius of gyration k, and S represents the angle of the rifling; this factor may be ignored in the subsequent calculations as small, less than I %.

00The importance of a study of the changes of the vis viva depending on squares of velocities, or what is now called the "kinetic energy" of a system, was recognized in Newton's time, especially by Leibnitz; and it was perceived (at any rate for special cases) that an increase in this quantity in the course of any motion of the system was otherwise expressible by what we now call the "work" done by the forces.

00The energy of a system is the measure of its capacity for doing work, on the assumption of suitable connexions with other systems. When the motion of a body is checked by a spring, its kinetic energy being destroyed, the spring, if perfectly elastic, is capable of restoring the motion; but if it is checked by friction no such restoration can be immediately effected.

00On certain assumptions required for the extension of the methods of the kinetic theory of gases to liquids, L.

00We can calculate, by the help of the kinetic theory and the theory of chances, the frequency with which the necessary conjunctions of ions will occur, and show that the general law will be that the coagulative powers should be in the ratios of 1: x: x 2.

004, which, according to the kinetic theory, is an indication that an important fraction of the energy absorbed is devoted to rotation or vibration.

00It is much more probable that heat is really the kinetic energy of motion of the molecules, and is passed on from one to another by collisions.

00The high conductivity of metals is then explained by the small mass and high velocity of diffusion of these electric atoms. Assuming the kinetic energy of an electric atom at any temperature to be equal to that of a gaseous molecule, its velocity, on Sir J.

00On the kinetic theory the molecules of a gas are relatively far apart and there is nothing analogous to friction between two adjacent layers A and B moving with different velocities.

00This potential energy becomes kinetic when the slag is brought into contact with lime in the presence of water, and causes the formation of a true hydraulic silicate of lime.

00Thus The Direct Experimental Evidence Is Somewhat Meagre And Conflicting, But The Question Of The Relation Of The Specific Heats Of Gases Is One Of Great Interest In Connexion With The Kinetic Theory And The Constitution Of The Molecule.

00According To The Elementary Kinetic Theory Of An Ideal Gas, The Molecules Of Which Are So Small And So Far Apart That Their Mutual Actions May Be Neglected, The Kinetic Energy Of Translation Of The Molecules Is Proportional To The Absolute Temperature, And Is Equal To 3/2 Of Pv, The Product Of The Pressure And The Volume, Per Unit Mass.

00If The Molecules Are Supposed To Be Like Smooth, Hard, Elastic Spheres, Incapable Of Receiving Any Other Kind Of Energy Except That Of Translation, The Specific Heat At Constant Volume Would Be The Increase Per Degree Of The Kinetic Energy Namely 3Pv/20=3R/2, That At Constant Pressure Would Be 5R/2, And The Ratio Of The Specific Heats Would Be 5/3 Or 1.666.

00In 1879 Maxwell Considered It One Of The Greatest Difficulties Which The Kinetic Theory Had Yet Encountered, That In Spite Of The Many Other Degrees Of Freedom Of Vibration Revealed By The Spectroscope, The Experimental Value Of The Ratio S/S Was 1.40 For So Many Gases, Instead Of Being Less Than 4/3.

00When Bosanquet says that in " Heat is a mode of motion " there is no reference to individual objects, but " a pure hypothetical form which absolutely neglects the existence of objects," he falls far short of expressing the nature of this scientific judgment, for in his Theory of Heat Clerk Maxwell describes it as " believing heat as it exists in a hot body to be in the form of kinetic energy."

00If steam or vapour is " wire-drawn " or expanded through a porous plug or throttling aperture without external loss or gain of heat, the total heat (E+pv) remains constant (Thermodynamics, § I I), provided that the experiment is arranged so that the kinetic energy of flow is the same on either side of the throttle.

00The mass-system is then said to possess kinetic symmetry about 0.

00Young in connection with the kinetic theory of the tides, where the same point arises.

00The product 4muf is called the kinetic energy of the particle, and the equation.

00(21) is therefore equivalent to the statement that the increment of the kinetic energy is equal to the work done on the particle.

00which asserts that when no extraneous forces act the sum of the kinetic and potential energies is constant.

00be to increase the sum of the kinetic and potential energies by an amount equal to the work done by them.

00If we assume that there is no loss of apparent kinetic energy we have also miuii +miuf2 = miui2 +mfuzi.

00It follows from the formula 15 (10) for the internal kinetic energy of a system of particles that as a result of the impact this energy is diminished by the amount i m1mi 2(1 _ei)m+m(ui_uf)1.

00The unit of work on the same principles is ML2T2, and itis to be noticed that this is identical with the unit of kinetic energy.

00Next consider the kinetic energy of the system.

00the total kinetic energy is equal to the kinetic energy of the whole mass supposed concentrated at G and moving with this point, together with the kinetic energy of the motion relative to G.

00The latter may be called the internal kinetic energy of the system.

00which expresses the internal kinetic energy in terms of the relative velocities of the several pairs of particles.

00Also by (10) the internal kinetic energy is - m,m~

00mif-mi The increase of the kinetic energy of the system in any interval of time will of course be equal to the total work done by all the forces acting on the particles.

00If T denote the kinetic energy, we may say then that the sum T + V is in any interval of time increased by an amount equal to the work done by the extraneous forces.

00The increase of the kinetic energy of a rigid body in any interval of time is equal to the work done by the extraneous forces acting on the body.

00(13) The left-hand side is the kinetic energy of the whole mass, supposed concentrated at G and moving with this point, together with the kinetic energy of the motion relative to G (15); and the right-hand member represents the integral work done by the extraneous forces in the successive infinitesimal displacements into which the motion may be resolved.

00the kinetic energy is 3/4MK262+

00If q be any variable co-ordinate defining the position or (in the case of a system of bodies) the configuration, the velocity of each particle at any instant will be proportional to 4, and the total kinetic energy may be expressed in the form 1/8A42, where A is in general a function of q The special case where both cones are right circular and a is constant is important ~n astronomy and also in mechanism (theory of bevel wheels).

00If m be the mass of a particle at P, and PN the perpendicular to the instantaneous axis, the kinetic energy T is given by 2T=2~{m(w.

00In this case the kinetic energy is given by 2T = M0 (u1 +v2+w1) +AP2 +Bq2 +Cr2 2Fqr 2Grp 2Hpq, (13) where M0 is the mass, and A, B, C, F, G, H are the moments and products of inertia with respect to the mass-centre; cf.

00Hence the change of kinetic energy is TT=~.1/8(u+u) +n.1/8(v+v)+1.1/8(w+w),

00We are thus led to the following statement: the change of kinetic energy due to any system of impulsive forces is equal to the sum of the products of the several forces into the semisum of the initial and final velocities of their respective points of application, resolved in the directions of the forces.

0077 the kinetic energy generated is ~M (ic2H- Cq2)cuf, if C be the instantaneous centre; this is seen to be equal to ~F.

00The kinetic energy T of the motion relative to 0 will be constant.

00Motion of a Solid of Revolution.In the case of a solid of revolution, or (more generally) whenever there is kinetic syminetry about an asks through the mass-centre, or through a fixec point 0, a number of interesting problems can be treated almost directly from first principles.

00If the direction of the axis of kinetic symmetry be specified by means of the angular co-ordinates 0, ~

00kinetic energy is given by 2T=A(O2+sinO ~2)+Cnh.

00The former is, in fact, equal to 2T, and the latter to ~2, where T is the kinetic energy an.d r the resultant angular momentum.

00If OA, OB, OC be principal axes of inertia of a solid, and if A, B, C denote the corresponding moments of inertia, the kinetic energy is given by 2TA(~ sin 4,sin 0 cos 44~)2+B Ce cos 4,+sin0 sin$)i +C (~+cos0~)2.

00This equation expresses that the kinetic energy is increasing at a rate equal to that at which work is being done by the forces.

00To apply the equations (11) to the case of the top we start with the expression (15) of 22 for the kinetic energy, the simplified form (i) of 20 being for the present purpose inadmissible, since it is essential that the generalized co-ordinates employed should be competent to specify the position of every particle.

00Connecting the experimental study of the physical and chemical properties is the immense theoretical edifice termed the kinetic theory of gases.

00But no one can tell whether the study of physiological phenomena in general, and of nervous phenomena in particular, will not reveal to us, besides the vis viva or kinetic energy of which Leibnitz spoke, and the potential energy which was a later and necessary adjunct, some new kind of energy which may differ from the other two by rebelling against calculation" (Bergson, Time and Free Will, Eng.

00203) show that chemical action is to be referred to the latter of these vectors, but whether Fresnel's or Neumann's hypothesis be correct is only to be decided when we know if it be the mean kinetic energy or the mean potential energy that determines chemical action.

00Ann., 1875), who regarded electricity as consisting of atoms much smaller than those of matter, and supposed that heat was the kinetic energy of these electric atoms. If we suppose that an electric current in a metal is a flow of negative electric atoms in one direction, the positive electricity associated with the far heavier material atoms remaining practically stationary, and if the atomic heat of electricity is of the same order as that of an equivalent quantity of hydrogen or any other element, the heat carried per ampere-second at o C., namely P, would be of the order of 030 of a joule, which would be ample to account for all the observed effects on the convection theory.

00Coulomb pointed out long ago that the resistance of a body to be set in motion was in many cases much greater than the resistance which it offered to continued motion; and since his time writers have always distinguished the "friction of rest," or static friction, from the "friction of motion," or kinetic friction.

00These experiments distinctly point to the conclusion, although without absolutely proving it, that in such cases the coefficient of kinetic friction gradually increases as the velocity becomes extremely small, and passes without discontinuity into that of static friction.

00Kinetic an crystallographic analysis of the key active site acid/base arginine in a soluble fumarate reductase.

00Identification of the active site acid/base catalyst in a bacterial fumarate reductase: a kinetic and crystallographic study.

00The high kinetic energies are needed to overcome the repulsion of the two positive nuclei.

00It slows down, losing kinetic energy as its potential energy, of electrical repulsion, increases in compensation.

00Kinetic sculptures by Jean Tinguely are on display to 24th September.

00These kinetic differences were confirmed by short-term in vitro culture both in fetal calf serum and in AS.

00Q: Is bug splat only for kinetic weapons?

00Kinetic and thermodynamic stabilization will be provided via extensive spin delocalization and substituent electronic effects.

00

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