In physics, angular momentum is the rotational analog of linear momentum. It is an important physical quantity because it is a conserved quantity—the total angular momentum of a closed system remains constant. Angular momentum has both a direction and a magnitude, and both are conserved. Bicycles and motorcycles, frisbees rifled bullets, and gyroscopes owe their useful properties to conservation of angular momentum. Conservation of angular momentum is also why hurricanes form spirals and neutron stars have high rotational rates. In general, conservation limits the possible motion of a system, but it does not uniquely determine it.
The radian, denoted by the symbol rad, is the unit of angle in the International System of Units (SI) and is the standard unit of angular measure used in many areas of mathematics. The unit was formerly an SI supplementary unit. The radian is defined in the SI as being a dimensionless unit, with 1 rad = 1. Its symbol is accordingly often omitted, especially in mathematical writing.
The Mössbauer effect, or recoilless nuclear resonance fluorescence, is a physical phenomenon discovered by Rudolf Mössbauer in 1958. It involves the resonant and recoil-free emission and absorption of gamma radiation by atomic nuclei bound in a solid. Its main application is in Mössbauer spectroscopy.
Newton's laws of motion are three basic laws of classical mechanics that describe the relationship between the motion of an object and the forces acting on it. These laws can be paraphrased as follows:
- A body remains at rest, or in motion at a constant speed in a straight line, unless acted upon by a force.
- When a body is acted upon by a force, the time rate of change of its momentum equals the force.
- If two bodies exert forces on each other, these forces have the same magnitude but opposite directions.
The Trouton–Noble experiment was an attempt to detect motion of the Earth through the luminiferous aether, and was conducted in 1901–1903 by Frederick Thomas Trouton and H. R. Noble. It was based on a suggestion by George FitzGerald that a charged parallel-plate capacitor moving through the aether should orient itself perpendicular to the motion. Like the earlier Michelson–Morley experiment, Trouton and Noble obtained a null result: no motion relative to the aether could be detected. This null result was reproduced, with increasing sensitivity, by Rudolf Tomaschek, Chase and Hayden in 1994. Such experimental results are now seen, consistent with special relativity, to reflect the validity of the principle of relativity and the absence of any absolute rest frame. The experiment is a test of special relativity.
In the physical science of dynamics, rigid-body dynamics studies the movement of systems of interconnected bodies under the action of external forces. The assumption that the bodies are rigid simplifies analysis, by reducing the parameters that describe the configuration of the system to the translation and rotation of reference frames attached to each body. This excludes bodies that display fluid, highly elastic, and plastic behavior.
The word "mass" has two meanings in special relativity: invariant mass is an invariant quantity which is the same for all observers in all reference frames, while the relativistic mass is dependent on the velocity of the observer. According to the concept of mass–energy equivalence, invariant mass is equivalent to rest energy, while relativistic mass is equivalent to relativistic energy.
In classical mechanics, the Laplace–Runge–Lenz (LRL) vector is a vector used chiefly to describe the shape and orientation of the orbit of one astronomical body around another, such as a binary star or a planet revolving around a star. For two bodies interacting by Newtonian gravity, the LRL vector is a constant of motion, meaning that it is the same no matter where it is calculated on the orbit; equivalently, the LRL vector is said to be conserved. More generally, the LRL vector is conserved in all problems in which two bodies interact by a central force that varies as the inverse square of the distance between them; such problems are called Kepler problems.
The Stern–Gerlach experiment demonstrated that the spatial orientation of angular momentum is quantized. Thus an atomic-scale system was shown to have intrinsically quantum properties. In the original experiment, silver atoms were sent through a spatially varying magnetic field, which deflected them before they struck a detector screen, such as a glass slide. Particles with non-zero magnetic moment are deflected, due to the magnetic field gradient, from a straight path. The screen reveals discrete points of accumulation, rather than a continuous distribution, owing to their quantized spin. Historically, this experiment was decisive in convincing physicists of the reality of angular-momentum quantization in all atomic-scale systems.
In classical mechanics, areal velocity is a pseudovector whose length equals the rate of change at which area is swept out by a particle as it moves along a curve. In the adjoining figure, suppose that a particle moves along the blue curve. At a certain time t, the particle is located at point B, and a short while later, at time t + Δt, the particle has moved to point C. The region swept out by the particle is shaded in green in the figure, bounded by the line segments AB and AC and the curve along which the particle moves. The areal velocity magnitude is this region's area divided by the time interval Δt in the limit that Δt becomes vanishingly small. The vector direction is postulated normal to the plane containing the position and velocity vectors of the particle, following a convention known as the right hand rule.
The ladder paradox is a thought experiment in special relativity. It involves a ladder, parallel to the ground, travelling horizontally at relativistic speed and therefore undergoing a Lorentz length contraction. The ladder is imagined passing through the open front and rear doors of a garage or barn which is shorter than its rest length, so if the ladder was not moving it would not be able to fit inside. To a stationary observer, due to the contraction, the moving ladder is able to fit entirely inside the building as it passes through. On the other hand, from the point of view of an observer moving with the ladder, the ladder will not be contracted, and it is the building which will be Lorentz contracted to an even smaller length. Therefore, the ladder will not be able to fit inside the building as it passes through. This poses an apparent discrepancy between the realities of both observers.
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. The unification of SR with quantum mechanics is relativistic quantum mechanics, while attempts for that of GR is quantum gravity, an unsolved problem in physics.
The Ehrenfest paradox concerns the rotation of a "rigid" disc in the theory of relativity.
Bell's spaceship paradox is a thought experiment in special relativity. It was designed by E. Dewan and M. Beran in 1959 and became more widely known when J. S. Bell included a modified version. A delicate thread hangs between two spaceships. They start accelerating simultaneously and equally as measured in the inertial frame S, thus having the same velocity at all times as viewed from S. Therefore, they are all subject to the same Lorentz contraction, so the entire assembly seems to be equally contracted in the S frame with respect to the length at the start. At first sight, it might appear that the thread will not break during acceleration.
Rotation around a fixed axis is a special case of rotational motion. The fixed-axis hypothesis excludes the possibility of an axis changing its orientation and cannot describe such phenomena as wobbling or precession. According to Euler's rotation theorem, simultaneous rotation along a number of stationary axes at the same time is impossible; if two rotations are forced at the same time, a new axis of rotation will appear.
A pendulum is a body suspended from a fixed support so that it swings freely back and forth under the influence of gravity. When a pendulum is displaced sideways from its resting, equilibrium position, it is subject to a restoring force due to gravity that will accelerate it back toward the equilibrium position. When released, the restoring force acting on the pendulum's mass causes it to oscillate about the equilibrium position, swinging it back and forth. The mathematics of pendulums are in general quite complicated. Simplifying assumptions can be made, which in the case of a simple pendulum allow the equations of motion to be solved analytically for small-angle oscillations.
The swinging Atwood's machine (SAM) is a mechanism that resembles a simple Atwood's machine except that one of the masses is allowed to swing in a two-dimensional plane, producing a dynamical system that is chaotic for some system parameters and initial conditions.
Michał Gryziński was a Polish nuclear physicist, plasma physics specialist and the founder of the free-fall atomic model, an alternative theoretical formulation, a classical approximation asking for trajectories of electron averaging to probability densities described by quantum mechanics.
Tests of relativistic energy and momentum are aimed at measuring the relativistic expressions for energy, momentum, and mass. According to special relativity, the properties of particles moving approximately at the speed of light significantly deviate from the predictions of Newtonian mechanics. For instance, the speed of light cannot be reached by massive particles.
The physics of a bouncing ball concerns the physical behaviour of bouncing balls, particularly its motion before, during, and after impact against the surface of another body. Several aspects of a bouncing ball's behaviour serve as an introduction to mechanics in high school or undergraduate level physics courses. However, the exact modelling of the behaviour is complex and of interest in sports engineering.
