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Reference: Beginning Physics I

CHAPTER 1: INTRODUCTION & MATHEMATICAL BACKGROUND

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KEY WORD LIST

Physics, Science, Mathematics, Absolute value, Variables, Function, Graph, Inverse function, Trigonometric Function, Simultaneous equations, Linear equation, Units, Standard, International System of Units (SI), Significant figures, Scientific notation

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GLOSSARY

For details on the following concepts, please consult CHAPTER 1.

PHYSICS
Origin: “pertaining to nature.” Physics is the science that deals with matter, energy, motion, and force.

SCIENCE
Origin: “to know.” Science is systematic knowledge of the physical or material world gained through observation and experimentation.

MATHEMATICS
Origin: “something learned.” Mathematics is the systematic treatment of magnitude, relationships between figures and forms, and relations between quantities expressed symbolically.

ABSOLUTE VALUE
The value without regards to its sign.  It is the magnitude of a number.

VARIABLES
Variables are quantities that can take on a range of values.

FUNCTION
Origin: “performed, executed.” A function is a mathematical relationship between two variables. If one of the variables takes on a particular value, the relationship tells us the corresponding value of the other variable.

GRAPH
Whenever one has a mathematical relationship between two variables, one can represent the function by a two dimensional graph. Note: Look up the definitions of the following on page 3: axes, origin, independent variable, dependent variable, slope, intercept.

INVERSE FUNCTION
A function gives us a y value for every x value. Inverse function turns it around and gives us an x value for every y-value. To get the graph of inverse function, rotate the graph of the function 90 deg clockwise so that y appears along the horizontal.

TRIGONOMETRIC FUNCTION
Trigonometric Functions are most usually defined in terms of ratios of sides of a right triangle, in which the angle plays the role of the independent variable.

SIMULTANEOUS EQUATIONS
When we have two different relationships involving the same two variables, then both relationships can be valid only for specific values of the variables.

LINEAR EQUATION
Such equation are represented by straight lines on a graph.

UNITS
Origin: “unity.” Unit is an identity element. We need units of measurement to measure physical quantities, such as, length, area, volume, velocity, acceleration, mass, time and temperature. Not all measurable quantities require their own units. Often, the unit is automatically defined in terms of other units. Such units are called derived units. In the subject of mechanics, only three physical quantities must have their units defined independently. These three quantities are usually taken to be length, mass and time, and their units are called  fundamental units. It turns out that units can be treated algebraically in any physics equation.

STANDARD
The physical specimen, which defines the unit, is called the standard.

INTERNATIONAL SYSTEM OF UNITS (SI)
The set of units most commonly used throughout the world, and which is almost exclusively used in scientific work. In mechanics, the units are the meter, the kilogram, and the second, and are what is commonly called the mks system.

SIGNIFICANT FIGURES
Whenever a measured value is given for a physical quantity, it can only be an approximation, because it is not possible to measure  anything with “infinite” accuracy. A scientist or engineer who specifies the numerical value of a physical quantity keeps only as many figures in the number as are justified by the accuracy to which the physical quantity is known. For any measured quantity there is always some uncertainty in the last digit given. The number of significant figures provide a rough measure of percent uncertainty.

SCIENTIFIC NOTATION
Scientific notation is a method for expressing a given quantity as a number having significant digits necessary for a specified degree of accuracy, multiplied by 10 to the appropriate power, as 1385.62 written as 1.386 × 10³.

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