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Velocity
The velocity of an object is the rate of change of its position with respect to a frame of reference, and is a function of time. Velocity is equivalent to a specification of its speed and direction of motion (e.g. 7001600000000000000♠60 km/h to the north). Velocity
Velocity
is an important concept in kinematics, the branch of classical mechanics that describes the motion of bodies. Velocity
Velocity
is a physical vector quantity; both magnitude and direction are needed to define it. The scalar absolute value (magnitude) of velocity is called "speed", being a coherent derived unit whose quantity is measured in the SI (metric system) as metres per second (m/s) or as the SI base unit of (m⋅s−1). For example, "5 metres per second" is a scalar, whereas "5 metres per second east" is a vector
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Meter
The metre (British spelling and BIPM spelling[1]) or meter (American spelling) (from the French unit mètre, from the Greek noun μέτρον, "measure") is the base unit of length in some metric systems, including the International System of Units
International System of Units
(SI). The SI unit symbol is m.[2] The metre is defined as the length of the path travelled by light in a vacuum in 1/299 792 458 second.[1] The metre was originally defined in 1793 as one ten-millionth of the distance from the equator to the North Pole. In 1799, it was redefined in terms of a prototype metre bar (the actual bar used was changed in 1889). In 1960, the metre was redefined in terms of a certain number of wavelengths of a certain emission line of krypton-86. In 1983, the current definition was adopted. The imperial inch is defined as 0.0254 metres (2.54 centimetres or 25.4 millimetres). One metre is about ​3 3⁄8 inches longer than a yard, i.e
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Statistical Mechanics
Statistical mechanics
Statistical mechanics
is a branch of theoretical physics that uses probability theory to study the average behaviour of a mechanical system whose exact state is uncertain.[1][2][3][note 1] Statistical mechanics
Statistical mechanics
is commonly used to explain the thermodynamic behaviour of large systems. This branch of statistical mechanics, which treats and extends classical thermodynamics, is known as statistical thermodynamics or equilibrium statistical mechanics. Microscopic mechanical laws do not contain concepts such as temperature, heat, or entropy; however, statistical mechanics shows how these concepts arise from the natural uncertainty about the state of a system when that system is prepared in practice
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Second
The second is the SI base unit
SI base unit
of time, commonly understood and historically defined as 1/86,400 of a day – this factor derived from the division of the day first into 24 hours, then to 60 minutes and finally to 60 seconds each. Another intuitive understanding is that it is about the time between beats of a human heart.[nb 1] Mechanical and electric clocks and watches usually have a face with 60 tickmarks representing seconds and minutes, traversed by a second hand and minute hand. Digital clocks and watches often have a two-digit counter that cycles through seconds
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SI Unit
The International System of Units
International System of Units
(SI, abbreviated from the French Système international (d'unités)) is the modern form of the metric system, and is the most widely used system of measurement. It comprises a coherent system of units of measurement built on seven base units (ampere, kelvin, second, metre, kilogram, candela, mole) and a set of twenty decimal prefixes to the unit names and unit symbols that may be used when specifying multiples and fractions of the units. The system also specifies names for 22 derived units for other common physical quantities like lumen, watt, etc. The base units, except for one, are derived from invariant constants of nature, such as the speed of light and the triple point of water, which can be observed and measured with great accuracy
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Udwadia–Kalaba Equation
In theoretical physics, the Udwadia–Kalaba equation [1] is a method for deriving the equations of motion of a constrained mechanical system. This equation was discovered by Firdaus E. Udwadia and Robert E. Kalaba in 1992. The fundamental equation is the simplest and most comprehensive equation so far discovered [2] for writing down the equations of motion of a constrained mechanical system. It makes a convenient distinction between externally applied forces and the internal forces of constraint, similar to the use of constraints in Lagrangian mechanics, but without the use of Lagrange multipliers. The Udwadia–Kalaba equation applies to a wide class of constraints, both holonomic constraints and nonholonomic ones, as long as they are linear with respect to the accelerations
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Statics
Statics is the branch of mechanics that is concerned with the analysis of loads (force and torque, or "moment") acting on physical systems that do not experience an acceleration (a=0), but rather, are in static equilibrium with their environment. When in static equilibrium, the acceleration of the system is zero and the system is either at rest, or its center of mass moves at constant velocity. The application of Newton's second law
Newton's second law
to a system gives: F = m a . displaystyle textbf F =m textbf a ,. Where bold font indicates a vector that has magnitude and direction. F is the total of the forces acting on the system, m is the mass of the system and a is the acceleration of the system. The summation of forces will give the direction and the magnitude of the acceleration will be inversely proportional to the mass
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Damping
In engineering, the damping ratio is a dimensionless measure describing how oscillations in a system decay after a disturbance. Many systems exhibit oscillatory behavior when they are disturbed from their position of static equilibrium. A mass suspended from a spring, for example, might, if pulled and released, bounce up and down. On each bounce, the system is trying to return to its equilibrium position, but overshoots it. Sometimes losses (e.g. frictional) damp the system and can cause the oscillations to gradually decay in amplitude towards zero or attenuate
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Potential Energy
U = m · g · h (gravitational) U = ½ · k · x2 U = ½ · C · V2 (electric) U = -m · B (magnetic)Part of a series of articles aboutClassical mechanics F → = m a → displaystyle vec F =m vec a Second law of motionHistory TimelineBranchesApplied Celestial Continuum Dynamics Kinematics Kinetics Statics StatisticalFundamentalsAcceleration Angular momentum Couple D'Alembert's principle Energykinetic potentialForce Frame of reference Inertial frame of reference Impulse Inertia / Moment of inertia MassMechanical power Mechanical workMoment Momentum Space Speed Time Torque Velocity Virtual workFormulationsNewton's laws of motionAnalytical mechanicsLagrangian mechanics Hamiltonian mechanics Routhian mechanics Hamilton–Jacobi equation Appell's equation of m
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Energy
In physics, energy is the quantitative property that must be transferred to an object in order to perform work on, or to heat, the object.[note 1] Energy
Energy
is a conserved quantity; the law of conservation of energy states that energy can be converted in form, but not created or destroyed. The SI unit of energy is the joule, which is the energy transferred to an object by the work of moving it a distance of 1 metre against a force of 1 newton. Common forms of energy include the kinetic energy of a moving object, the potential energy stored by an object's position in a force field (gravitational, electric or magnetic), the elastic energy stored by stretching solid objects, the chemical energy released when a fuel burns, the radiant energy carried by light, and the thermal energy due to an object's temperature. Mass
Mass
and energy are closely related
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Virtual Work
Virtual work
Virtual work
arises in the application of the principle of least action to the study of forces and movement of a mechanical system. The work of a force acting on a particle as it moves along a displacement will be different for different displacements. Among all the possible displacements that a particle may follow, called virtual displacements, one will minimize the action. This displacement is therefore the displacement followed by the particle according to the principle of least action
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Couple (mechanics)
In mechanics, a couple is a system of forces with a resultant (a.k.a. net or sum) moment but no resultant force.[1] A better term is force couple or pure moment. Its effect is to create rotation without translation, or more generally without any acceleration of the centre of mass. In rigid body mechanics, force couples are free vectors, meaning their effects on a body are independent of the point of application. The resultant moment of a couple is called a torque. This is not to be confused with the term torque as it is used in physics, where it is merely a synonym of moment.[2] Instead, torque is a special case of moment
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Analytical Mechanics
In theoretical physics and mathematical physics, analytical mechanics, or theoretical mechanics is a collection of closely related alternative formulations of classical mechanics. It was developed by many scientists and mathematicians during the 18th century and onward, after Newtonian mechanics. Since Newtonian mechanics
Newtonian mechanics
considers vector quantities of motion, particularly accelerations, momenta, forces, of the constituents of the system, an alternative name for the mechanics governed by Newton's laws
Newton's laws
and Euler's laws is vectorial mechanics. By contrast, analytical mechanics uses scalar properties of motion representing the system as a whole—usually its total kinetic energy and potential energy—not Newton's vectorial forces of individual particles.[1] A scalar is a quantity, whereas a vector is represented by quantity and direction
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Damping Ratio
In engineering, the damping ratio is a dimensionless measure describing how oscillations in a system decay after a disturbance. Many systems exhibit oscillatory behavior when they are disturbed from their position of static equilibrium. A mass suspended from a spring, for example, might, if pulled and released, bounce up and down. On each bounce, the system is trying to return to its equilibrium position, but overshoots it. Sometimes losses (e.g. frictional) damp the system and can cause the oscillations to gradually decay in amplitude towards zero or attenuate
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Hamiltonian Mechanics
Hamiltonian mechanics is a theory developed as a reformulation of classical mechanics and predicts the same outcomes as non-Hamiltonian classical mechanics. It uses a different mathematical formalism, providing a more abstract understanding of the theory
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Moment (physics)
In physics, a moment is an expression involving the product of a distance and a physical quantity, and in this way it accounts for how the physical quantity is located or arranged. Moments are usually defined with respect to a fixed reference point; they deal with physical quantities as measured at some distance from that reference point. For example, the moment of force acting on an object, often called torque, is the product of the force and the distance from a reference point. In principle, any physical quantity can be multiplied by distance to produce a moment; commonly used quantities include forces, masses, and electric charge distributions.Contents1 History 2 Elaboration2.1 Examples3 Multipole moments 4 Applications of multipole moments 5 See also 6 References 7 External linksHistory[edit] The concept of moment in physics is derived from the mathematical concept of moments.[1] [clarification needed]
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