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Relativistic Mechanics
In physics, relativistic mechanics refers to mechanics compatible with special relativity (SR) and general relativity (GR). It provides a non-quantum mechanical description of a system of particles, or of a fluid, in cases where the velocities of moving objects are comparable to the speed of light c. As a result, classical mechanics is extended correctly to particles traveling at high velocities and energies, and provides a consistent inclusion of electromagnetism with the mechanics of particles. This was not possible in Galilean relativity, where it would be permitted for particles and light to travel at any speed, including faster than light. The foundations of relativistic mechanics are the postulates of special relativity and general relativity
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Mass In Special Relativity
Mass
Mass
in special relativity incorporates the general understandings from the laws of motion of special relativity along with its concept of mass–energy equivalence. The word mass is given two meanings in special relativity: one (rest or invariant mass, and its equivalent rest energy) is an invariant quantity which is the same for all observers in all reference frames; the other (relativistic mass or the equivalent total energy of the body) is dependent on the velocity of the observer. The term relativistic mass tends not to be used in particle and nuclear physics and is often avoided by writers on special relativity.[1] They do, however, talk about the (total) energy of a body, which is the equivalent to its relativistic mass, rather than the rest energy equivalent to its rest mass. The measurable inertia and gravitational attraction of a body in a given frame of reference is determined by its relativistic mass, not merely its rest mass
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Space And Time
In physics, spacetime is any mathematical model that fuses the three dimensions of space and the one dimension of time into a single four-dimensional continuum. Spacetime
Spacetime
diagrams can be used to visualize relativistic effects such as why different observers perceive where and when events occur. Until the turn of the 20th century, the assumption had been that the three-dimensional geometry of the universe (its spatial expression in terms of coordinates, distances, and directions) was independent of one-dimensional time
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Observer (physics)
If Wiktionary
Wiktionary
has a definition already, change this tag to TWCleanup2 or else consider a soft redirect to Wiktionary
Wiktionary
by replacing the text on this page with Wi
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Frames Of Reference
In physics, a frame of reference (or reference frame) consists of an abstract coordinate system and the set of physical reference points that uniquely fix (locate and orient) the coordinate system and standardize measurements. In n dimensions, n+1 reference points are sufficient to fully define a reference frame. Using rectangular (Cartesian) coordinates, a reference frame may be defined with a reference point at the origin and a reference point at one unit distance along each of the n coordinate axes. In Einsteinian relativity, reference frames are used to specify the relationship between a moving observer and the phenomenon or phenomena under observation. In this context, the phrase often becomes "observational frame of reference" (or "observational reference frame"), which implies that the observer is at rest in the frame, although not necessarily located at its origin
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Time Derivative
A time derivative is a derivative of a function with respect to time, usually interpreted as the rate of change of the value of the function.[1] The variable denoting time is usually written as t displaystyle t, .Contents1 Notation 2 Use in physics2.1 Example: circular motion3 In differential geometry 4 Use in economics 5 See also 6 ReferencesNotation[edit] A variety of notations are used to denote the time derivative. In addition to the normal (Leibniz's) notation, d x d t displaystyle frac dx dt A very common short-hand notation used, especially in physics, is the 'over-dot'
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Newton's Second Law
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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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 M
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Line Integral
In mathematics, a line integral is an integral where the function to be integrated is evaluated along a curve. The terms path integral, curve integral, and curvilinear integral are also used; contour integral as well, although that is typically reserved for line integrals in the complex plane. The function to be integrated may be a scalar field or a vector field. The value of the line integral is the sum of values of the field at all points on the curve, weighted by some scalar function on the curve (commonly arc length or, for a vector field, the scalar product of the vector field with a differential vector in the curve). This weighting distinguishes the line integral from simpler integrals defined on intervals. Many simple formulae in physics (for example, W = F · s) have natural continuous analogs in terms of line integrals (W = ∫C F · ds)
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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
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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Frame Of Reference
In physics, a frame of reference (or reference frame) consists of an abstract coordinate system and the set of physical reference points that uniquely fix (locate and orient) the coordinate system and standardize measurements. In n dimensions, n+1 reference points are sufficient to fully define a reference frame. Using rectangular (Cartesian) coordinates, a reference frame may be defined with a reference point at the origin and a reference point at one unit distance along each of the n coordinate axes. In Einsteinian relativity, reference frames are used to specify the relationship between a moving observer and the phenomenon or phenomena under observation. In this context, the phrase often becomes "observational frame of reference" (or "observational reference frame"), which implies that the observer is at rest in the frame, although not necessarily located at its origin
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Mass
Mass
Mass
is both a property of a physical body and a measure of its resistance to acceleration (a change in its state of motion) when a net force is applied.[1] It also determines the strength of its mutual gravitational attraction to other bodies. The basic SI unit
SI unit
of mass is the kilogram (kg). In physics, mass is not the same as weight, even though mass is often determined by measuring the object's weight using a spring scale, rather than balance scale comparing it directly with known masses. An object on the Moon
Moon
would weigh less than it does on Earth
Earth
because of the lower gravity, but it would still have the same mass. This is because weight is a force, while mass is the property that (along with gravity) determines the strength of this force. In Newtonian physics, mass can be generalized as the amount of matter in an object
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Force
In physics, a force is any interaction that, when unopposed, will change the motion of an object.[1] A force can cause an object with mass to change its velocity (which includes to begin moving from a state of rest), i.e., to accelerate. Force
Force
can also be described intuitively as a push or a pull. A force has both magnitude and direction, making it a vector quantity. It is measured in the SI unit of newtons and represented by the symbol F. The original form of Newton's second law
Newton's second law
states that the net force acting upon an object is equal to the rate at which its momentum changes with time
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Center Of Mass
In physics, the center of mass of a distribution of mass in space is the unique point where the weighted relative position of the distributed mass sums to zero, or the point where if a force is applied it moves in the direction of the force without rotating. The distribution of mass is balanced around the center of mass and the average of the weighted position coordinates of the distributed mass defines its coordinates. Calculations in mechanics are often simplified when formulated with respect to the center of mass. It is a hypothetical point where entire mass of an object may be assumed to be concentrated to visualise its motion. In other words, the center of mass is the particle equivalent of a given object for application of Newton's laws of motion. In the case of a single rigid body, the center of mass is fixed in relation to the body, and if the body has uniform density, it will be located at the centroid
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Three-dimensional
Three-dimensional space
Three-dimensional space
(also: 3-space or, rarely, tri-dimensional space) is a geometric setting in which three values (called parameters) are required to determine the position of an element (i.e., point). This is the informal meaning of the term dimension. In physics and mathematics, a sequence of n numbers can be understood as a location in n-dimensional space. When n = 3, the set of all such locations is called three-dimensional Euclidean space. It is commonly represented by the symbol ℝ3. This serves as a three-parameter model of the physical universe (that is, the spatial part, without considering time) in which all known matter exists. However, this space is only one example of a large variety of spaces in three dimensions called 3-manifolds
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