moment

In engineering mechanics, bending (also known as flexure) characterizes the behavior of a structural element subjected to a lateral load. A structural element subjected to bending is known as a beam. A closet rod sagging under the weight of clothes on clothes hangers is an example of a beam experiencing bending. Bending produces reactive forces inside a beam as the beam attempts to accommodate the flexural load: in the case of the beam in Figure 1, the material at the top of the beam is being compressed while the materia ...

Including:

• Bending - Stress in a beam

Read more here: » Bending: Encyclopedia - Bending

A counterweight is a weight that balances a load. They are often used in traction lifts (elevators), cranes, and funfair rides. If the counterweight were not there, the load would tend to tip the crane forwards [clockwise]. The counterweight, which is usually made of a dense material such as concrete or lead, provides an anticlockwise moment that balances the load on the crane. What's more: When the load is lifted, the counterweig ...

Read more here: » Counterweight: Encyclopedia - Counterweight

A V10 is an engine in V configuration, having 10 cylinders in two banks of five. V10 - Mechanicals. The V10 configuration is inherently imbalanced in the vertical plane and generates a rocking moment causing vibration from end to end of the engine. To contain this issue a balance shaft is required. Theoretically, the best V-angle is 72°; with this angle there is no vibration in vertical and transverse directions. The complexity of designing this made the V10 difficult to engineer without computer-a ...

Including:

• V10 - Mechanicals
• V10 - Road cars
• V10 - Racing

Read more here: » V10: Encyclopedia - V10

In combinatorial mathematics, the nth Bell number, named in honor of Eric Temple Bell, is the number of partitions of a set with n members, or equivalently, the number of equivalence relations on it. Starting with B0 = B1 = 1, the first few Bell numbers are (sequence A000110 in OEIS): 1, 1, 2, 5, 15, 52, 203, 877, 4140, 21147, 115975 (See also breakdown by number of subsets/equivalence classes.) Bell number - Partitions of a set. I ...

Including:

• Bell number - Partitions of a set
• Bell number - Another view of Bell numbers
• Bell number - Properties of Bell numbers
• Bell number - Triangle scheme for calculating Bell numbers

Read more here: » Bell number: Encyclopedia - Bell number

Ailerons are hinged flaps attached to the trailing edge of an airplane wing, usually near the wingtips. They are used to control the aircraft in roll. The two ailerons are interconnected so that one goes down when the other goes up: the downgoing aileron increases the lift on its wing while the upgoing aileron reduces the lift on the other wing, producing a rolling moment about the aircraft's longitudinal axis. The wo ...

Read more here: » Aileron: Encyclopedia - Aileron

In physics, torque can be thought of informally as "rotational force". Torque is measured in units of newton metres, and its symbol is τ. The concept of Torque, also called moment or couple, originated with the work of Archimedes on levers. The rotational analogues of force, mass and acceleration are torque, moment of inertia and angular acceleration respectively. The force applied to a lever, multiplied by its distance from the lever's fulcrum, is the torque. For example, a force of three newtons applied two metres fro ...

Including:

• Torque - Units
• Torque - Special cases and other facts
• Torque - Moment arm formula
• Torque - Force at an angle
• Torque - Static equilibrium
• Torque - Torque as a function of time
• Torque - Machine torque
• Torque - Relationship between torque and power
• Torque - Conversion to other units
• Torque - Derivation

Read more here: » Torque: Encyclopedia - Torque

White noise (Sample ▶ (help·info)) is a random signal (or process) with a flat power spectral density. In other words, the signal's power spectral density has equal power in any band, at any centre frequency, having a given bandwidth. An infinite-bandwidth white noise signal is purely a theoretical construct. By having power at all frequencies, the total power of such a signal is infinite. In practice, a signal can be "white" with a flat spectrum over ...

Including:

• White noise - Statistical properties
• White noise - Colors of noise
• White noise - Applications
• White noise - Mathematical definition
• White noise - White random vector
• White noise - White random process white noise
• White noise - Random vector transformations
• White noise - Simulating a random vector
• White noise - Whitening a random vector
• White noise - Random signal transformations
• White noise - Simulating a continuous-time random signal
• White noise - Whitening a continuous-time random signal
• White noise - External link

Read more here: » White noise: Encyclopedia - White noise

A dam is a barrier across flowing water that obstructs, directs or retards the flow, often creating a reservoir, lake or impoundment. Most dams have a section called a spillway or weir over which or through which it is intended that water will flow either intermittently or continuously. Dam - Types of dams. Dams may be classified according to structure, intended purpose or height. Based on structure and material used, dams are classified as timber dams, embankment dams or masonry ...

Including:

• Dam - Types of dams
• Dam - Diversionary dams
• Dam - Timber dams
• Dam - Embankment dams
• Dam - Masonry dams
• Dam - Cofferdams
• Dam - Spillways
• Dam - Other considerations
• Dam - Environmental impacts
• Dam - Stream flow
• Dam - Barrier to migration
• Dam - Water quality impacts
• Dam - Examples of dams
• Dam - Failed dams

Read more here: » Dam: Encyclopedia - Dam

Central limit theorems are a set of weak-convergence results in probability theory. Intuitively, they all express the fact that any sum of many independent identically distributed random variables will tend to be distributed according to a particular "attractor distribution". The most important and famous result is called simply The Central Limit Theorem which states that if the sum of the variables has a finite variance, then it will be approximately normally distributed. Since many real processes yield distributions with finite vari ...

Including:

• Central limit theorem - Classical central limit theorem
• Central limit theorem - Proof of the central limit theorem
• Central limit theorem - Convergence to the limit
• Central limit theorem - Alternative statements of the theorem
• Central limit theorem - Lyapunov condition
• Central limit theorem - Lindeberg condition
• Central limit theorem - Non-independent case

Read more here: » Central limit theorem: Encyclopedia - Central limit theorem

An earthquake is a sudden and sometimes catastrophic movement of a part of the Earth's surface. Earthquakes result from the dynamic release of elastic strain energy that radiates seismic waves. Earthquakes typically result from the movement of faults, planar zones of deformation within the Earth's upper crust. The word earthquake is also widely used to indicate the source region itself. The Earth's lithosphere is a patch work of plates in slow but constant motion (see plate tectonics). Earthquakes occur where the stress resulting from ...

Including:

• Earthquake - Characteristics
• Earthquake - Earthquake Size
• Earthquake - Causes
• Earthquake - Preparation for earthquakes
• Earthquake - Specific fault articles
• Earthquake - Specific earthquake articles

Read more here: » Earthquake: Encyclopedia - Earthquake

Due to an inability to resist deformation, fluids exert pressure normal to any contacting surface. In addition, when the fluid is at rest (static) that pressure is isotropic, i.e. it acts with equal magnitude in all directions. This characteristic allows fluids to transmit force through the length of pipes or tubes, i.e., a force applied to a fluid in a pipe is transmitted, via the fluid, to the other end of the pipe. If the force is unequal, t ...

See also:

Fluid statics, Fluid statics - Static pressure in fluids, Fluid statics - Hydrostatic pressure, Fluid statics - Atmospheric pressure, Fluid statics - Buoyancy, Fluid statics - Stability, Fluid statics - Liquids-fluids with free surfaces, Fluid statics - Surface tension effects

Read more here: » Fluid statics: Encyclopedia II - Fluid statics - Static pressure in fluids

Internal energy U cannot be measured directly. There is an arbitrary zero reference value, just as there is for gravitational potential energy. Only its change ΔU can be measured, and this is where Q is heat added to the system (measured in joules in SI) ±W is work done on the system (measured in joules in SI) ΔU is the value of the internal energy after a process minus its value before, independent of the arbitrary sign convention used for the second ter ...

See also:

Internal energy, Internal energy - Measurement

Read more here: » Internal energy: Encyclopedia II - Internal energy - Measurement

The weak law of large numbers states that if X1, X2, X3, ... is an infinite sequence of random variables, where all the random variables have the same expected value μ and variance σ2; and are uncorrelated (i.e., the correlation between any two of them is zero), then the sample average converges in probability to μ. Somewhat less tersely: For any positive number ε, no matter how small, we have < ...

See also:

Law of large numbers, Law of large numbers - The weak law, Law of large numbers - Proof, Law of large numbers - The strong law, Law of large numbers - A weaker law and proof

Read more here: » Law of large numbers: Encyclopedia II - Law of large numbers - The weak law

The information contained in n independent Bernoulli trials, each with probability of success θ, may be calculated as follows. (The outcome is random and can be either of two possible outcomes called "success" and "failure" and can be thought of as flipping a coin with the probability of flipping a "head" is θ and the probability of flipping a "tail" is 1 − θ.) In the following, A ...

See also:

Fisher information, Fisher information - Matrix form, Fisher information - For multivariate normal distribution, Fisher information - Example: single parameter, Fisher information - Physical information, Fisher information - Books

Read more here: » Fisher information: Encyclopedia II - Fisher information - Example: single parameter

The property of ferromagnetism is due to the direct influence of two effects from quantum mechanics: spin and the Pauli exclusion principle. The spin of an electron, combined with its orbital angular momentum, results in a magnetic dipole moment and creates a magnetic field. (The classical analogue of quantum-mechanical spin is a spinning ball of charge, but the quantum version has distinct differences, such as the fact that it has discrete up/down states that are not described by a vector; similarly for "orbital" motion, whose classi ...

See also:

Ferromagnetism, Ferromagnetism - Ferromagnetic materials, Ferromagnetism - Physical origin, Ferromagnetism - Unusual ferromagnetism

Read more here: » Ferromagnetism: Encyclopedia II - Ferromagnetism - Physical origin

Eckhart Tolle - Mechanics of the Mind. There appear to be many bodies of thought about what it means to be human. The complexity of modern psychology added to older bodies of thought stemming from religion make for a dizzying and perhaps baffling prospect towards understanding what being human is. As it turns out, there is a simple mechanism that is underneath all of this. This article is about that “Machine of the Mind.” The Simplicity of the Machine What we think, feel, see and experience as people is a sim ...

See also:

Eckhart Tolle, Eckhart Tolle - Teachings, Eckhart Tolle - Mechanics of the Mind, Eckhart Tolle - Imagination, Eckhart Tolle - Emotion, Eckhart Tolle - Body Feeling, Eckhart Tolle - Words and actions, Eckhart Tolle - The Machine is broken, Eckhart Tolle - What you don’t know can hurt you and probably does, Eckhart Tolle - Awareness is the key, Eckhart Tolle - Know pain know gain!, Eckhart Tolle - The alternative, Eckhart Tolle - Focus and Expansion, Eckhart Tolle - Happiness as a consequence not as a goal, Eckhart Tolle - Summary and conclusion, Eckhart Tolle - Works, Eckhart Tolle - Books, Eckhart Tolle - Audio tapes

Read more here: » Eckhart Tolle: Encyclopedia II - Eckhart Tolle - Teachings

Leonhard Euler was born near Basel, Switzerland, the son of Paul Euler, a Lutheran minister. Although in his childhood he exhibited great mathematical talents, his father wanted him to study theology and become a minister. In 1720 Euler began his studies at the University of Basel. There Euler met Daniel and Nikolaus Bernoulli, who noticed Euler's skills in mathematics. Paul Euler had attended Jakob Bernoulli's mathematical lectures and respected his family. When Daniel and Nikolaus Bernoulli asked him to allow his son to study mathematics he finally ...

See also:

Leonhard Euler, Leonhard Euler - Biography, Leonhard Euler - Discoveries, Leonhard Euler - Honours, Leonhard Euler - Quotes

Read more here: » Leonhard Euler: Encyclopedia II - Leonhard Euler - Biography

Moments are often estimated based on the sample moments without estimating the probability distribution first. ...

See also:

Moment mathematics, Moment mathematics - Sample moments

Read more here: » Moment mathematics: Encyclopedia II - Moment mathematics - Sample moments

The n-th raw moment is defined as the expected value of kn: The series on the right is just a series representation of the Riemann zeta function, but it only converges for values of s-n that are greater than unity. Thus: Note that the ratio of the zeta functions is well defined, even for because the series representation of the zeta function can be analytically continued. This does not change the fact that the moments are specified by the series itself, an ...

See also:

Zeta distribution, Zeta distribution - Moments, Zeta distribution - Moment generating function, Zeta distribution - The case s = 1

Read more here: » Zeta distribution: Encyclopedia II - Zeta distribution - Moments

A physical dipole consists of two equal and opposite point charges: literally, two poles. Its field at large distances (i.e., distances large in comparison to the separation of the poles) depends almost entirely on the dipole moment as defined above. A point (electric) dipole is the limit obtained by letting the separation tend to 0 while keeping the dipole moment fixed. The field of a point dipole has a particularly simple form, and ...

See also:

Dipole, Dipole - Alignment of a dipole to an applied field, Dipole - Physical dipoles point dipoles and approximate dipoles, Dipole - Molecular dipoles, Dipole - Field from a magnetic dipole, Dipole - Magnitude, Dipole - Vector form, Dipole - Magnetic vector potential, Dipole - Field from an electric dipole, Dipole - Electrostatic potential, Dipole - Dipole radiation

Read more here: » Dipole: Encyclopedia II - Dipole - Physical dipoles point dipoles and approximate dipoles