OpenLLM-France/wikimedia huggingface dataset:
# Pinyin/Broccoli

Special:search/broccoli prefix:Pinyin/
Broccoli is a plant. It is a vegetable similar to cabbage. Broccoli has green flower heads and a stalk. It comes from Mexico and is one of the most bought vegetables in England.
Xīlánhuā shì zhíwù, lèisì yēcài de shūcài. Xīlánhuā yǒu lǜsè de huātóu hé huājīng, yuánzì Mexico, shì Yīngguó xiāoliàng zuìduō de shūcài zhīyī.
# Pinyin/Embassy

Search Pinyin embassy
# Pinyin/Emotional

See also
# Pinyin/Electronic commerce

Diànzǐ shāngwù
# Pinyin/Elementary algebra

Elementary algebra is a simple algebra. Arithmetic only has numbers and operations (such as: addition, subtraction, multiplication, and division), while algebra also uses symbols (e.g.: x, y, or a, b) to represent numbers. The symbols are called variables.
Chūděng dàishù shì jiǎndān de dàishù. Suànshù zhǐyǒu shùzì jíqí yùnsuàn (rú: jiā, jiǎn, chéng, chú), ér dàishù yě huì shǐyòng fúhào (rú: x, y huò a, b) lái biǎoshì shùzì, zhèxiē fúhào jiàozuò biànshù.
# How To Build a Pinewood Derby Car/Dimensions and specifications

* Home
* Preface
* Rules
* Block
* Wheels
* Axles
* Assembly
* Physics
* Appendices
Block
* Height: 1.25"
* Width: 1.75"
* Length: 7.0"
Weight
* Total: 5.000 oz.
* Wheels 3.6 g (stock, 1.0 g minimum practical)
Wheelbase
    Front Overhang 1.781" (1-25/32")
    Rear Overhang 0.813 (13/16")
    Overhang 0.625" (5/8")
Track
* Lanes: 2-6+
* Starting Height:4 ft. (variable)
* Lane Guide
    Width 1.625"
    Height 0.25"
    32 ft. (typical wood)
    40+ ft. (typical aluminum)
* Orthographic projection of a Pinewood Derby car block
* Diagram of pinewood derby car block with standard BSA wheelbase.
* Pinewood derby car design template for standard wheelbase PDF
* Diagram of pinewood derby car block with extended wheelbase.
* Pinewood derby car design template for extended wheelbase PDF
* Dimensions of a stock BSA wheel
* Dimensions of a stock pinewood derby axle.
# How To Build a Pinewood Derby Car

* Home
* Preface
* Rules
* Block
* Wheels
* Axles
* Assembly
* Physics
* Appendices
Pinewood derby cars are made from kits containing a wood block, plastic wheels and metal nails for axles. The completed cars race down a multi-lane track powered by gravity and slowed by friction and wind resistance. Pinewood Derby and related races are run by Boy Scouts of America's Cub Scouts, Awana Grand Prix, Royal Rangers, Shape N Race, Kub Kar Rally, Royal Ambassadors, and others.
          Pinewood derby racer modeled on Richard Petty's famous Plymouth Superbird
Construction of a pinewood derby car involves:
* cutting out the body
* adding weight
* filing and polishing the axles
* truing and polishing the wheels
* final alignment and assembly
A number of "speed secrets" have developed over the past half-century of pinewood derby. This book covers the hows, whys and even the physics and chemistry of this race, including
* rear biased weight
* lead, tungsten and zinc weights
* extended wheelbase
* raised front wheel
* coned wheels
* light wheels
* wheel molds
* plastic polish
* H and V tread
* beveled axles
* notched axles
* metal polish
* shimming and alignment
* graphite, moly, and liquid lubricants
* and how to paint the wheel spokes silver.
This book is for kids who will be working with adults to construct their cars, for parents who will be working with their kids and purchasing tools, parts and supplies, and for race organizers who will be writing the rules, inspecting the cars and running the races.
# How To Build a Pinewood Derby Car/Appendices

* Home
* Preface
* Rules
* Block
* Wheels
* Axles
* Assembly
* Physics
* Appendices
Appendices
* Dimensions and specifications
* Glossary
* Tools
* Links
# Fixed Rectangular Coordinate Frame

In this coordinate system, vectors are expressed as an addition of vectors in the x, y, and z direction from a non-rotating origin. Usually ${\vec {i}}\,\!$ is a unit vector in the x direction, ${\vec {j}}\,\!$ is a unit vector in the y direction, and ${\vec {k}}\,\!$ is a unit vector in the z direction.
The position vector, ${\vec {s}}\,\!$ (or ${\vec {r}}\,\!$), the velocity vector, ${\vec {v}}\,\!$, and the acceleration vector, ${\vec {a}}\,\!$ are expressed using rectangular coordinates in the following way:
${\vec {s}}=x{\vec {i}}+y{\vec {j}}+z{\vec {k}}\,\!$
${\vec {v}}={\dot {s}}={\dot {x}}{\vec {i}}+{\dot {y}}{\vec {j}}+{\dot {z}}{\vec {k}}\,\!$
${\vec {a}}={\ddot {s}}={\ddot {x}}{\vec {i}}+{\ddot {y}}{\vec {j}}+{\ddot {z}}{\vec {k}}\,\!$
Note: ${\dot {x}}={\frac {dx}{dt}}$ , ${\ddot {x}}={\frac {d^{2}x}{dt^{2}}}$
# Kinematics/Linear Motion
## Problems

* 1. A man fires a rock out of a slingshot directly upward. The rock has an initial velocity of 15 m/s. How long will it take for the rock to return to the level he fired it at?
* 5 It takes a man ten seconds to ride down an escalator. It takes the same man 15 seconds to walk back up the escalator against its motion. How long will it take the man to walk down the escalator at the same rate he was walking before?
Prerequisite: Calculus
* 24. Starting with the definitions of velocity and acceleration derive the kinematics equation for constant acceleration x = x0 + v0t + (1/2) at^2.
* 25. A cockroach starts 1 cm away from a wall. It starts running in a line directly away from the wall with a velocity of 1 cm/s, acceleration of 1 cm/s^2, jerk (d^3 x/dt^3) of 1 cm/s^3, d^4 x/dt^4 of 1 cm/s^4, and so on. How far is the cockroach from the wall after one second?

## Solutions

1. 3 s. Use the kinematics equation y = y0 + v0t + 1/2 at^2. Let the rock's initial height y be 0. Plugging the values into the equation yields 0 = 15t - (1/2) 10t^2. Factoring and solving for t yields solutions of 0 s and 3 s. Hence it takes the rock 3 s to return to its original height.
24. The quickest solution is to write the Taylor series for x, this yields the solution immediately. Another route to the solution is to solve the differential equation by separating the variables.
25. e cm. The Taylor series for positions is x = x0 + v0 t + (1/2!) a0 t^2 + (1/3!) j0 t^3 + ... . Since x0, v0, a0, ... are all equal to one and t, t^2, t^3, ... are all equal to one, you have the following series: x = 1 + 1 + 1/2 + 1/6 + ... . This is a series that sums to e, thus the cockroach travels e cm after one second.
# Kinematics/Prerequisites
## Prerequisites

The start of every course is always the stating of prerequisites. To start off this book requires a firm understanding of the following:
- Algebra
- Geometry and Trigonometry
- Calculus
- Vector Algebra/Calculus
All of the above required for this book will be covered in Chapter 0, a review chapter highlighting the mathematics required for this book.
If you are fairly confident that you already know all of the prerequisites, please take the mathematics review test at the end of Chapter 0.
If you score 80% or higher, go ahead to Chapter 1 and begin your studies.
# Kinematics/Sample Problems
## Sample problem related to curvilinear motion

Q.1) The motion of a body varies with the following equation:
$S=t^{3}-3t^{2}+6t+1\,\!$
a) Find the velocity and acceleration at $t=4secs\,\!$.
b) Find the maximum or minimum velocity experienced during its motion.
Ans) The given curve is displacement versus time curve.
          $S=t^{3}-3t^{2}+6t+1\,\!$
       So, the velocity is given by
          $V={\frac {ds}{dt}}=3t^{2}-6t+6\,\!$
       And so, acceleration is
          $a={\frac {d^{2}s}{dt^{2}}}=6t-6\,\!$
       Proceed for the problem by substituting the instant at which you need the variables..
          For maximum or minimum velocity, use the concepts of MAXIMA AND MINIMA from mathematics, which makes use of derivatives.

## Projectile motion

Q.2) An F-22 bomber is under a training session in the deserts of Iran. It is moving horizontally parallel to the ground at a speed of 1000kmph and at an altitude of 2400 meters. to bomb an target which is an mimic of an antiaircraft gun.
a)At what point from the antiaircraft gun should the bomber release the bomb so as to hit the target?
b)Now, if this becomes a real warfare scenario, and the anti aircraft gun's gears are blocked so that it is fixed at an angle of ${60}^{o}\,\!$ with the horizontal, and its muzzle velocity is 600m/sec, when should the antiaircraft gun fire a shell so as to hit the target??
# Kinematics
## Preface

    Introduction
Kinematics is the branch of physics dealing with the motion of particles or bodies. It defines movement at the level of position, velocity and acceleration, without incorporating masses and forces.
    Prerequisites
A proper study of the subject requires an understanding of 2D and 3D vectors. Of course you also need to review basic algebra, trigonometry and calculus. A proper understanding of kinematics require an understanding of vector calculus too.
    Sample Problems

## Chapter 0: A Mathematics Review

* Algebra Review
* Geometry and Trig Review
* Calculus Review
* Vector Review

## Chapter 1: Plane Kinematics

* 1D Coordinate Systems
* 2D Coordinate Systems
* Linear Motion
* Transformations

## Chapter 2: Kinematics in Three Space

* 3D Coordinate Systems
* Particles

## Two Dimensional Kinematics
### Displacement, Velocity, and Acceleration

Displacement is the change in position with respect to the frame of reference. In the case of a car moving on a road, the displacement is the change in position with respect to the road. This is important because the Earth itself is rotating and orbiting at considerable speed, which you do not notice due to inertia. Since omnipotence is not possible, all observations are made from a specific frame of reference. Displacement is usually expressed as a length measurement. Velocity is the change in displacement with respect to a change in time. The velocity of an object is again relative to the frame of reference. Acceleration is the change in velocity with respect to a change in time.
Therefore, we know that, for functions for displacement, velocity, and acceleration, respectively d, v, t :
    $d(t)=\int _{0}^{t}v(x)dx$
    $v(t)={\frac {dd}{dt}}=\int _{0}^{t}a(x)dx$
    $a(t)={\frac {dv}{dt}}$

### Kinematics Formulas

Using the above can create the basic kinematics formulas(subject to acceleration being constant):
    $x=x_{0}+v_{0}t+{\frac {1}{2}}at^{2}$
    $v=v_{0}+at$
    $v^{2}=v_{0}^{2}+2ax$

## Applications of Kinematics
### Motion

Motion is by far the simplest application of Kinematics, and uses the formulas with no adaptation.

#### Example 1
### Gravity and Falling Objects

Gravity affects most all earthly motion, and therefore is discussed first. Gravity pulls all objects the same distance from the earth with equal acceleration, regardless of mass, as discovered by Galileo in his famous test on the Leaning Tower of Pisa. In this section we will assume that friction and air resistance are negligible.
The standard gravity constant, 'g', is the is equal to 9.8m/s$^2$, and is the acceleration done by the earth's gravity at sea level. Therefore, a falling object fall accelerating at rate g. When using this with the Kinematics formulas, g replaces a.

#### Example 1

Show that the force (F) of a body is directly proportional to its momentum
# Kinematics/Algebra Review
## Algebra Review

- Variables, Equations, Polynomials and Systems
Imagine we are describing the location of a car. We could use two variables, x and y, to give its location in terms of longitude (x) and latitude (y). If we want to see how the car moves over the course of a day, we can include a variable for time, t. Then, measuring the longitude and latitude of the car over the day, we can express the position at a given time, x(t) and y(t). Here x and y depend on t, and thus are dependent variables. Time continues on its merry way, independent of any other variable.
For example, x = 3 would mean that x is equal to, or x is, 3. x = y would mean that x is equal to y, or x is, y. A re-arrangement, x - y = 0, is an equation that is both homogeneous and linear. Whenever two expressions are equal, one may be directly substituted for the other in an equation.
The general rule to remember is that you perform the reverse operation on the other side of the equation.
An example is 5x + 3 = 96, you would first move 3 to the other side, using +'s reverse operator -: 5x = 96 - 3 = 93
And then divide by 5, using the reverse operator of multiplication, division: x = 93/5
The equations: x + y = 5 2x + 3y = 2 form a system of linear equations; solving them is a matter of using a substitution. (Though this is not the only method of solving them, other methods are beyond the scope of this book)
For example, let's use the substitution that y = 5 - x (From the first equation), we can then do the following: 2x + 3y = 2 2x + 3(5 - x) = 2
Expanding the bracket, by multiplying everything inside it by 3, yields: 2x + 15 - 3x = 2 -x + 15 = 2 -x = -13 x = 13
You now have one variable's solution; finding y's solution is using the initial substitution: y = 5 - x = 5 - 13 = -8 You now have the solution set (13, -8)
To be continued...
# Kinematics/Introduction

Kinematics is the branch of mechanics that studies the motion of a body or a system of bodies without consideration given to its mass or the forces acting on it. Although it excludes forces and statics, they will be included within this wikibook regardless. This wikibook aims to take a more informal approach towards explaining the subject of kinematics and forces using mathematical derivations and such.
# Pinyin/Count

See also
# Pinyin/Coronary heart disease

Search Pinyin coronary
Search Pinyin heart
# Pinyin/Could

See also
# Pinyin/Corruption

See also
# Pinyin/Coronavirus

See also
# Pinyin/Coronavirus Infection

Search infection
Coronaviruses are a large family of viruses that includes viruses that may cause a range of illnesses in humans, from the common cold to SARS. Viruses of this family also cause a number of animal diseases.
Novel coronavirus is a particular strain of coronavirus that has not been previously identified in humans. There is very limited information on transmission, severity and clinical impact with only a small number of cases reported thus far.
Guānzhuàngbìngdú shǔyú yī lèi dàxíng jiāzú bìngdú, bāokuò zài rénlèi yǐnqǐ de yīxìliè jíbìng, cóng pǔtōng de gǎnmào zhì yánzhòng de SARS. Gāi jiāzú de bìngdú yě yǐnqǐ yīxiē dòngwù jíbìng.
Xīnxíng guānzhuàngbìngdú shǔyú guānzhuàngbìngdú de yī zhǒng tèbié lèixíng, wèicéng zài rénlèi fāxiàn. Yǒuguān bìngdú chuánbō, yánzhòng chéngdù yǐjí línchuáng yǐngxiǎng de xìnxī shífēn yǒuxiàn, mùqián zhǐyǒu shǎoliàng bìnglì bàogào.
# Mechanics of Materials

Author(s): Aaron D. Mazzeo

## Chapters and Syllabus for Printable PDF

* Background
* 1. Introduction to Mechanics of Materials
* 2. Physical Units and Standards
* 3. Static Equilibrium
** 3.1 Free Body Diagrams
** 3.2 Static Form of Newton's Second Law of Motion
** 3.3 Static Equilibrium of Trusses
** 3.4 Static Equilibrium of Beams
* 4. Axial Loading
** 4.1 Bars as Springs
** 4.2 Axially Loaded Bars in Series and Parallel
** 4.3 Indeterminate Axial Loading of Bars
* 5. Stress and Strain
** 5.1 Normal Stress
** 5.2 Shear Stress
** 5.3 Normal Strain
** 5.4 Shear Strain
** 5.5 Stress and Strain in a Bar
* 6. Material Properties
** 6.1 Stress-Strain Relationships for Ductile Materials
** 6.2 Stress-Strain Relationships for Brittle Materials
** 6.3 Poisson's Ratio
** 6.4 Modulus of Resilience
** 6.5 Fatigue
** 6.5 Uniaxial Failure from Yielding
** 6.6 Material Selection Charts
* 7. Material Testing
** 7.1 Tensile and Compressive Tests
** 7.2 Fatigue Testing
* 8. Torsion
** 8.1 Angular Displacement in a Twisted Rod
** 8.2 Shear Strain in a Twisted Rod
** 8.3 Elasticity of a Twisted Rod
* 9. Beam Bending
** 9.1 Relationship between Moment and Curvature
** 9.2 Displacement across a Beam
** 9.3 Statically Indeterminate Beams
** 9.4 Typical Beam Bending Conditions, Displacements, and Slopes
* 10. Combined Loading
** 10.1 Stress Transformations
** 10.2 Mohr's Circle for Stress
** 10.3 Shear Transformations
** 10.4 Mohr's Circle for Strain
* 11. Failure Criteria for Static Loading
** 11.1 Maximum Normal Stress
** 11.2 Maximum Shear Stress
** 11.3 Maximum Distortion Energy
** 11.4 Safety Factors
* 12. Pressure Vessels
* 13. Beam Buckling
# Mechanics of Materials/Background

This Wikibook is to provide living content for an undergraduate course in mechanics of materials or strength of materials. The material here will eventually be of sufficient quality and interest for self-learning or prescribed study by instructors/faculty members. One objective is that the material here would facilitate in-class discussions, group projects, or problem-solving that would leverage the instructors' expertise to enhance learning outcomes. Another objective is to facilitate students, instructors, professionals, and interested users adding/curating content to accommodate learning styles that might benefit from a spectrum of insights coming from learners and teachers with diverse backgrounds. The course will draw on material openly available with inspiration from key relevant texts. There is also a crowd-sourced mind map available (needs updating) on GitHub for this Wikibook on undergraduate mechanics of materials.
* ↑ Crandall, Stephen H.; Dahl, Norman C.; Lardner, Thomas J. (1999). An Introduction to the Mechanics of Solids (2nd ed.). McGraw-Hill.
* ↑ Eshbach, Ovid W., ed. (1936). Handbook of Engineering Fundamentals. John Wiley & Sons, Inc.
* ↑ Hibbeler, R. C. (2014). Mechanics of Materials. Prentice Hall.
* ↑ Norton, Robert L. (2014). Machine Design: An Integrated Approach (5th ed.). Prentice Hall.
* ↑ Ashby, Michael F.; Jones, David R. H. (1980). Engineering Materials 1: An Introduction to their Properties and Applications. International Series on Materials Science and Technology. Pergamon Press, Inc.
* ↑ Juvinall, Robert C.; Marshek, Kurt M. (2012). Fundamentals of Machine Component Design (5th ed.). John Wiley & Sons, Inc.
* ↑ Fogiel, Max, ed. (1999). The Handbook of Mechanical Engineering. Research & Education Association.
* ↑ Ucker, Jr., John J.; Pennock, Gordon R.; Shigley, Joseph E. (2017). Theory of Machines and Mechanisms (5th ed.). Oxford University Press.
* ↑ Shigley, Joseph Edward; Mitchell, Larry D. (1983). Mechanical Engineering Design (4th ed.). McGraw-Hill Book Company.
# Mechanics of Materials/Physical Units and Standards/Learning Problems on Physical Units and Standards
## 2.4 Learning Problems on Physical Units and Standards
### 2.4.1 Invitation to Contribute

We welcome contributions, as there is not a set cap on the number of illustrative examples/problems we include, nor do we care if the examples come from learners or instructors. We just ask that the problems be thoughtful and relevant. Contributors should also be open to a shuffling order or categorization of shown examples/problems.

### 2.4.2 Learning Objectives and Philosophy

The hope is that these problems will become part of in-class discussions, small-group learning, projects, or personal study. For classes in which instructors give graded exams, we encourage instructors to create original problems for the students to solve independently. After an exam, the instructors could make the problems available for others to study and add to open-source sites like this Wikibook. This pattern of teaching, learning, and assessment limits ethical concerns/temptations, strengthens the validity of course outcomes, and decreases the anxiety of honest learners who feel they go into exams at a disadvantage to others planning to refer to available databases of solved problems or real-time tutoring services. For engineering students, it also discourages rote memorization and an "arms race" to create an increasing number of "solutions manuals" that inevitably become public. No person or system is flawless or perfect, especially given the stresses and constraints on instructors and learners. Nonetheless, this open-source Wikibook aims to enhance open and transparent learning.

### 2.4.3 Illustrative Examples/Problems

Content Forthcoming
# Mechanisms

Welcome to the Mechanisms book! This book illustrates some of the simple and complex mechanisms that form the heart of many machines and engines.
It is intended to be accessible to everybody, however some mathematical derivation will be added to illustrate the concepts to those who are interested.

## Simple Mechanisms

* The Wheel
* The Lever
* Cams
* Gears
* Pistons
* Plain Bearings
* Ball Bearings
* Screw Thread
* A Wedge
* Hinges
* Universal Joints

## Internal Combustion Engines

The engines in which the process of combustion, or burning takes place internally(within the engine) to produce the movement of the required parts is known as an internal combustion engine.
* Four Stroke
* Two Stroke
* Wankel

## Stirling Engines

A type of engine which uses external combustion to heat one part and cool another, pumping heat from one to the other and outputting useful work, usually by means of a Crankshaft.

## Gear Trains

* Step Indexer

## Other resources
### External Websites

* Animated Engines
# 3.2 Static Form of Newton's Second Law of Motion

Newton's Second Law of Motion relates the sum of the forces on a body with a given mass to its acceleration. In the study of statics, we simply set this acceleration to zero meaning the body does not accelerate. When thinking about bridges and buildings, this condition may seem intuitively obvious but it is still worth pointing out that we do not want these structures to move.
# 3.1 Free Body Diagrams

In physics, we often employ free body diagrams (FBDs) to describe forces between objects and body forces. When thinking about the equilibrium of forces acting on an object/body, FBDs are a tremendous aid when used correctly. As shown in Figure 3.1, we can use a FBD on an object/body (the blue block on the inclined plane) to describe vectorial forces acting on the body (gravity, friction, and a normal force from the inclined plane). We can also describe action-reaction pairs of forces between objects using FBDs and remembering Newton's third law of motion. In the case of the block and inclined plane, we can envision one action-reaction pair as ${\vec {\mathsf {N}}}$ acting from the inclined plane against the blue block and the vectorial component from gravity with magnitude $mg\cos \theta$ acting from the block against the inclined plane. Another action-reaction pair would include the friction ${\vec {\mathsf {f}}}$ from the inclined plane acting on the block, along with the equal and opposite frictional force from the block acting on the inclined plane.
Identifying action-reaction pairs is key to understanding how the surrounding environment interacts with a structural object. When thinking of a free body as a particle or only having axial forces (i.e., forces going acting along an axis going through the centroid of a body), one might follow these steps:
* Define appropriate coordinate systems (e.g., XYZ, xyz).
* Draw vectors that describe the motion of the body -- usually none for stationary objects in statics/mechanics.
* Draw vectors for body forces acting on the body.
* Draw vectors for contact forces and surface forces acting on the body (i.e., select the force acting on the body from action-reaction pairs)
For this course, we envision most of our structures as fixed, unmoving sets of beams, trusses, or pressure vessels. Yes, these structures might be portions of moving vehicles, but the loading due to the acceleration will usually be minimal, unless there is rotation with high angular velocity (e.g. centripetal acceleration $r\omega ^{2}$ where $r$ is a radial distance and $\omega$ is an angular velocity).

### Body Forces or Contact Forces?

These questions explore the characteristics of body forces and contact forces.
Jumbo the Elephant would like to know which of the following are body forces.
Gravity
Friction
Electrostatic attraction
Centrifugal force :
Jumbo the Elephant would like to know which of the following are surface forces or contact forces.
Hydrostatic pressure.
Friction
Normal force
Shear force :
Go back to 3. Force-based Static Equilibrium.