Rigid body dynamics

The equation for particle linear momentum is where: m is the particle's mass. v is the particle's velocity. fi is one of the N forces acting on the particle. Assuming constant mass, this reduces to To generalize, assume a body of finite mass and size is composed of such particles. There exist internal forces, acting between any two particles, and external forces, acting only on the outside of the mass. Each particle has: ...

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Rigid body dynamics, Rigid body dynamics - Rigid body linear momentum, Rigid body dynamics - Rigid body angular momentum

Read more here: » Rigid body dynamics: Encyclopedia II - Rigid body dynamics - Rigid body linear momentum

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

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If a force is allowed to act through a distance, it is doing mechanical work. Similarly, if torque is allowed to act through a rotational distance, it is doing work. Power is the work per unit time. However, time and rotational distance are related by the angular speed where each revolution results in the circumference of the circle being travelled by the force that is generating the torque. This means that torque that is causing the angular speed to increase is doing work an ...

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Torque, 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

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Torque has dimensions of force times distance and the SI units of torque are stated as "newton-metres". Even though the order of "newton" and "metre" are mathematically interchangeable, the BIPM (Bureau International des Poids et Mesures) specifies that the order should be N·m not m·N[1]. The joule, the SI unit for energy or work, is also defined as 1 N·m, but this unit is not used for torque. Since energy can be thought of as the result of "force dot distance", energy is always a scalar whereas torque is "force cross distance" and ...

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Torque, 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 II - Torque - Units

Torque - Moment arm formula. A very useful special case, often given as the definition of torque in fields other than physics, is as follows: The construction of the "moment arm" is shown in the figure below, along with the vectors r and F mentioned above. The problem with this definition is that it does not give the direction of the torque but only the magnitude, and hence it is difficult to use in three-dimensional cases. If the force is perpendicular to the displacemen ...

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Torque, 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 II - Torque - Special cases and other facts

Torque is part of the basic specification of an engine: the power output of an engine is expressed as its torque multiplied by its rotational speed. Internal-combustion engines produce useful torque only over a limited range of rotational speeds (typically from around 1,000–6,000 rpm for a small car). The varying torque output over that range can be measured with a dynamometer, and shown as a torque curve. The peak of that torque curve usually occurs somewhat below the overall power peak. The torque peak cannot, by definition, ...

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Torque, 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 II - Torque - Machine torque

Craps (previously known as crabs) is a casino gambling game using dice. Players wager money against the casino on the outcome of one roll, or of a series of rolls of two dice. Craps can also be played in less formal settings and is said to be popular among soldiers. In such situations side bets are less frequent, with one or several participants covering or "fading" bets against the dice. Craps - The basic game. The basic game of craps is very simple. The most fundamental bet is the "pass line" wager ...

Including:

• Craps - The basic game
• Craps - Types of craps bets
• Craps - Other types of bets
• Craps - Examples of basic play
• Craps - Etiquette
• Craps - Rules related to casino security
• Craps - Commonly observed etiquette
• Craps - Odds
• Craps - Systems
• Craps - Dice Setting
• Craps - Dice Control
• Craps - Miscellaneous

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The fundamental bet in craps is the pass line bet, in which one bets that the dice will pass (that is, roll the point number before rolling a 7). The following discussion assumes that the shooter, as is usually the case, is betting on the pass line. If a point is made, most casinos allow pass line bettors to take odds by placing from one to five times (and at some casinos, up to 100 times) the pass line bet behind the line. This additional bet pays at the true odds, 2-to-1 if 4 or 10 is the point, 3-to-2 if 5 or 9 ...

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Craps, Craps - The basic game, Craps - Types of craps bets, Craps - Other types of bets, Craps - Examples of basic play, Craps - Etiquette, Craps - Rules related to casino security, Craps - Commonly observed etiquette, Craps - Odds, Craps - Systems, Craps - Dice Setting, Craps - Dice Control, Craps - Miscellaneous

Read more here: » Craps: Encyclopedia II - Craps - Types of craps bets

The basic game of craps is very simple. The most fundamental bet is the "pass line" wager, which almost everyone on a given game may make. On the first roll of the two dice (the come-out roll), the pass line bettors, or "right" bettors win by rolling either a 7 or 11 (a natural). If the shooter, or any other player, has a bet on the pass-line, he would win on the natural. Rolling craps (2, 3, or 12) loses immediately for the pass line bettor. Any other number (4, 5, 6, 8, 9, or 10) is called the point. To win, the ...

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Craps, Craps - The basic game, Craps - Types of craps bets, Craps - Other types of bets, Craps - Examples of basic play, Craps - Etiquette, Craps - Rules related to casino security, Craps - Commonly observed etiquette, Craps - Odds, Craps - Systems, Craps - Dice Setting, Craps - Dice Control, Craps - Miscellaneous

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Besides the rules of the actual game, certain unwritten rules of etiquette exist while playing craps and are expected to be followed. Many consider these guidelines as important as the actual rules themselves. New players should familiarize themselves with them before approaching a craps table. Craps - Rules related to casino security. Players are not supposed to handle the dice with more than one hand nor take the dice past the edge of the table. When throwing the dice, the player is expect ...

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Craps, Craps - The basic game, Craps - Types of craps bets, Craps - Other types of bets, Craps - Examples of basic play, Craps - Etiquette, Craps - Rules related to casino security, Craps - Commonly observed etiquette, Craps - Odds, Craps - Systems, Craps - Dice Setting, Craps - Dice Control, Craps - Miscellaneous

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Craps is such a popular game, its terminology is often found as colloquialisms in our language. The terms "on a roll", "crapshoot", "no dice", "crap out", "Snake Eyes" and "do it the hard way" all trace their origins to the game of craps. As casinos restrict players' options in blackjack, craps is increasing in popularity, as it offers the best odds of all standard casino games based on pure chance. The plot of the musical Guys and Dolls revolves around some illegal games of craps, w ...

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Craps, Craps - The basic game, Craps - Types of craps bets, Craps - Other types of bets, Craps - Examples of basic play, Craps - Etiquette, Craps - Rules related to casino security, Craps - Commonly observed etiquette, Craps - Odds, Craps - Systems, Craps - Dice Setting, Craps - Dice Control, Craps - Miscellaneous

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In fact, there is a small but dedicated community of controlled shooters that maintain records and claim proof of dice influencing in casino conditions. The concept of "controlled shooting" however goes far beyond "setting the dice". It purports to involve limiting the "degrees of freedom" in the Rigid body dynamics of the dice. A mechanical engineer, under the pseudonym "SharpShooter", wrote a book on the subject called "Get The Edge At Craps: How to Control the Dice", which claims to define the ...

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Craps, Craps - The basic game, Craps - Types of craps bets, Craps - Other types of bets, Craps - Examples of basic play, Craps - Etiquette, Craps - Rules related to casino security, Craps - Commonly observed etiquette, Craps - Odds, Craps - Systems, Craps - Dice Setting, Craps - Dice Control, Craps - Miscellaneous

Read more here: » Craps: Encyclopedia II - Craps - Dice Control

Various scam artists have, over the years, marketed "systems" that purportedly enabled players to beat the house. Such betting strategies do not work (or, more accurately, they work only for a player with infinite wealth who faces no maximum bet). One of the best known is the Martingale system where you start by betting $1 and doubling your bet whenever you lose; upon winning, you start over at $1. If you play this system, you will 1) risk losing $128 (or more, if you choose to continue despite mounting losses) to win $1; and 2) run up again ...

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Craps, Craps - The basic game, Craps - Types of craps bets, Craps - Other types of bets, Craps - Examples of basic play, Craps - Etiquette, Craps - Rules related to casino security, Craps - Commonly observed etiquette, Craps - Odds, Craps - Systems, Craps - Dice Setting, Craps - Dice Control, Craps - Miscellaneous

Read more here: » Craps: Encyclopedia II - Craps - Systems

The rules vary slightly from one casino to another, but the expected value of most bets is only slightly negative (the most favorable bets with the most favorable rules offer a house advantage of as little as 0.18%). All bets have a negative expectation, except the "free odds" bet with an expectation of 0, that the player is allowed to make after a point is established on a flat (line) bet. Since there is no correlation between die rolls, there is no possible winning strategy over any given period of time. While experienced blackjack players ...

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Craps, Craps - The basic game, Craps - Types of craps bets, Craps - Other types of bets, Craps - Examples of basic play, Craps - Etiquette, Craps - Rules related to casino security, Craps - Commonly observed etiquette, Craps - Odds, Craps - Systems, Craps - Dice Setting, Craps - Dice Control, Craps - Miscellaneous

Read more here: » Craps: Encyclopedia II - Craps - Odds