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Impulse (physics)
In classical mechanics, impulse (symbolized by J or Imp[1]) is the integral of a force, F, over the time interval, t, for which it acts. Since force is a vector quantity, impulse is also a vector in the same direction. Impulse applied to an object produces an equivalent vector change in its linear momentum, also in the same direction.[2] The SI unit of impulse is the newton second (N⋅s), and the dimensionally equivalent unit of momentum is the kilogram meter per second (kg⋅m/s). The corresponding English engineering units are the pound-second (lbf⋅s) and the slug-foot per second (slug⋅ft/s). A resultant force causes acceleration and a change in the velocity of the body for as long as it acts. A resultant force applied over a longer time therefore produces a bigger change in linear momentum than the same force applied briefly: the change in momentum is equal to the product of the average force and duration
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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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Newton (unit)
The newton (symbol: N) is the International System of Units
International System of Units
(SI) derived unit of force. It is named after Isaac Newton
Isaac Newton
in recognition of his work on classical mechanics, specifically Newton's second law of motion. See below for the conversion factors.Contents1 Definition 2 Examples 3 Commonly seen as kilonewtons 4 Conversion factors 5 See also 6 Notes and referencesDefinition[edit] One newton is the force needed to accelerate one kilogram of mass at the rate of one metre per second squared in direction of the applied force. In 1946, Conférence Générale des Poids et Mesures (CGPM) Resolution 2 standardized the unit of force in the MKS system of units to be the amount needed to accelerate 1 kilogram of mass at the rate of 1 metre per second squared
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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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Pound (force)
The pound-force (symbol: lbf[1], sometimes lbf,[2]) is a unit of force used in some systems of measurement including English Engineering units and the British Gravitational System.[3] Pound force should not be confused with foot-pounds or pound-feet, which are units of torque, and may be written as "lbf⋅ft". They should not be confused with pound-mass (symbol: lb), often simply called pounds, which is a unit of mass.Contents1 Definitions1.1 Product of avoirdupois pound and standard gravity2 Conversion to other units 3 Foot–pound–second (FPS) systems of units 4 See also 5 Notes 6 ReferencesDefinitions[edit] The pound-force is equal to the gravitational force exerted on a mass of one avoirdupois pound on the surface of Earth
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Conserved Quantities
In mathematics, a conserved quantity of a dynamical system is a function of the dependent variables whose value remains constant along each trajectory of the system.[1] Not all systems have conserved quantities, and conserved quantities are not unique, since one can always apply a function to a conserved quantity, such as adding a number. Since many laws of physics express some kind of conservation, conserved quantities commonly exist in mathematical models of physical systems
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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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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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Inertial Frame Of Reference
An inertial frame of reference, in classical physics, is a frame of reference in which bodies, whose net force acting upon them is zero, are not accelerated; that is they are at rest or they move at a constant velocity in a straight line.[1] In analytical terms, it is a frame of reference that describes time and space homogeneously, isotropically, and in a time-independent manner.[2] Conceptually, in classical physics and special relativity, the physics of a system in an inertial frame have no causes external to the system.[3] An inertial frame of reference may also be called an inertial reference frame, inertial frame, Galilean reference frame, or inertial space.[citation needed] All inertial frames are in a state of constant, rectilinear motion with respect to one another; an accelerometer moving with any of them would detect zero acceleration
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Inertia
Inertia
Inertia
is the resistance of any physical object to any change in its state of motion. This includes changes to the object's speed, direction, or state of rest. Inertia
Inertia
is also defined as the tendency of objects to keep moving in a straight line at a constant velocity. The principle of inertia is one of the fundamental principles in classical physics that are still used to describe the motion of objects and how they are affected by the applied forces on them. Inertia
Inertia
comes from the Latin word, iners, meaning idle, sluggish. Inertia
Inertia
is one of the primary manifestations of mass, which is a quantitative property of physical systems
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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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Space
Space
Space
is the boundless three-dimensional extent in which objects and events have relative position and direction.[1] Physical space is often conceived in three linear dimensions, although modern physicists usually consider it, with time, to be part of a boundless four-dimensional continuum known as spacetime. The concept of space is considered to be of fundamental importance to an understanding of the physical universe. However, disagreement continues between philosophers over whether it is itself an entity, a relationship between entities, or part of a conceptual framework. Debates concerning the nature, essence and the mode of existence of space date back to antiquity; namely, to treatises like the Timaeus of Plato, or Socrates
Socrates
in his reflections on what the Greeks called khôra (i.e
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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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Routhian Mechanics
In analytical mechanics, a branch of theoretical physics, Routhian mechanics is a hybrid formulation of Lagrangian mechanics
Lagrangian mechanics
and Hamiltonian mechanics developed by Edward John Routh. Correspondingly, the Routhian is the function which replaces both the Lagrangian and Hamiltonian functions. The Routhian, like the Hamiltonian, can be obtained from a Legendre transform of the Lagrangian, and has a similar mathematical form to the Hamiltonian, but is not exactly the same. The difference between the Lagrangian, Hamiltonian, and Routhian functions are their variables
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Lagrangian Mechanics
Lagrangian mechanics
Lagrangian mechanics
is a reformulation of classical mechanics, introduced by the Italian-French mathematician and astronomer Joseph-Louis Lagrange
Joseph-Louis Lagrange
in 1788. In Lagrangian mechanics, the trajectory of a system of particles is derived by solving the Lagrange equations in one of two forms, ei
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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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