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Friction
Friction
Friction
is the force resisting the relative motion of solid surfaces, fluid layers, and material elements sliding against each other.[2] There are several types of friction:Dry friction is a force that opposes the relative lateral motion of two solid surfaces in contact. Dry friction is subdivided into static friction ("stiction") between non-moving surfaces, and kinetic friction between moving surfaces
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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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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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Power (physics)
In physics, power is the rate of doing work, the amount of energy transferred per unit time. Having no direction, it is a scalar quantity. In the International System of Units, the unit of power is the joule per second (J/s), known as the watt in honour of James Watt, the eighteenth-century developer of the steam engine condenser. Another common and traditional measure is horsepower (comparing to the power of a horse). Being the rate of work, the equation for power can be written: power = work time displaystyle text power = frac text work text time The integral of power over time defines the work performed. Because this integral depends on the trajectory of the point of application of the force and torque, this calculation of work is said to be path dependent. As a physical concept, power requires both a change in the physical universe and a specified time in which the change occurs
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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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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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Hamilton–Jacobi Equation
In mathematics, the Hamilton–Jacobi equation (HJE) is a necessary condition describing extremal geometry in generalizations of problems from the calculus of variations, and is a special case of the Hamilton–Jacobi–Bellman equation. It is named for William Rowan Hamilton and Carl Gustav Jacob Jacobi. In physics, the Hamilton-Jacobi equation is an alternative formulation of classical mechanics, equivalent to other formulations such as Newton's laws of motion[citation needed], Lagrangian mechanics
Lagrangian mechanics
and Hamiltonian mechanics. The Hamilton–Jacobi equation is particularly useful in identifying conserved quantities for mechanical systems, which may be possible even when the mechanical problem itself cannot be solved completely. The HJE is also the only formulation of mechanics in which the motion of a particle can be represented as a wave
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Moment Of Inertia
The moment of inertia, otherwise known as the angular mass or rotational inertia, of a rigid body is a tensor that determines the torque needed for a desired angular acceleration about a rotational axis. It depends on the body's mass distribution and the axis chosen, with larger moments requiring more torque to change the body's rotation. It is an extensive (additive) property: For a point mass the moment of inertia is just the mass times the square of perpendicular distance to the rotation axis. The moment of inertia of a rigid composite system is the sum of the moments of inertia of its component subsystems (all taken about the same axis)
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Koopman–von Neumann Classical Mechanics
The Koopman–von Neumann mechanics is a description of classical mechanics in terms of Hilbert space, introduced by Bernard Koopman and John von Neumann
John von Neumann
in 1931 and 1932.[1][2][3] As Koopman and von Neumann demonstrated, a Hilbert space
Hilbert space
of complex, square integrable wavefunctions can be defined in which classical mechanics can be formulated as an operatorial theory similar to quantum mechanics.Contents1 History1.1 Ergodic theory2 Definition and dynamics2.1 Derivation starting from the Liouville equation 2.2 Derivation starting from operator axioms 2.3 Measurements3 KvN vs Liouville mechanics 4 Quantum analogy 5 See also 6 References 7 Further readingHistory[edit] Statistical mechanics
Statistical mechanics
describes macroscopic systems in terms of statistical ensembles, such as the macroscopic properties of an ideal gas
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Work (physics)
W = F ⋅ s W = τ θPart of a series of articles aboutClassical mechanics F → = m a → displaystyle vec F =m vec a Second
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 Mo
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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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Momentum
In Newtonian mechanics, linear momentum, translational momentum, or simply momentum (pl. momenta) is the product of the mass and velocity of an object. It can be more generally stated as a measure of how hard it is to stop a moving object. It is a three-dimensional vector quantity, possessing a magnitude and a direction. If m is an object's mass and v is the velocity (also a vector), then the momentum is p = m v , displaystyle mathbf p =mmathbf v , In SI units, it is measured in kilogram meters per second (kg⋅m/s). Newton's second law
Newton's second law
of motion states that a body's rate of change in momentum is equal to the net force acting on it. Momentum
Momentum
depends on the frame of reference, but in any inertial frame it is a conserved quantity, meaning that if a closed system is not affected by external forces, its total linear momentum does not change
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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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Speed
In everyday use and in kinematics, the speed of an object is the magnitude of its velocity (the rate of change of its position); it is thus a scalar quantity.[1] The average speed of an object in an interval of time is the distance travelled by the object divided by the duration of the interval;[2] the instantaneous speed is the limit of the average speed as the duration of the time interval approaches zero. Speed
Speed
has the dimensions of distance divided by time. The SI unit
SI unit
of speed is the metre per second, but the most common unit of speed in everyday usage is the kilometre per hour or, in the US and the UK, miles per hour
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Newton's Laws Of Motion
Newton's laws of motion
Newton's laws of motion
are three physical laws that, together, laid the foundation for classical mechanics. They describe the relationship between a body and the forces acting upon it, and its motion in response to those forces. More precisely, the first law defines the force qualitatively, the second law offers a quantitative measure of the force, and the third asserts that a single isolated force doesn't exist. These three laws have been expressed in several ways, over nearly three centuries,[1] and can be summarised as follows:First law: In an inertial frame of reference, an object either remains at rest or continues to move at a constant velocity, unless acted upon by a force.[2][3]Second law: In an inertial reference frame, the vector sum of the forces F on an object is equal to the mass m of that object multiplied by the acceleration a of the object: F = ma
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