Chapter 1: Units, Physical Quantities, and Vectors

Physical Laws

Physics is an experimental science. Physicists observe the phenomena of nature and try to find patterns that relate these phenomena. These patterns are called physical theories or, when they are very well established and widely used, physical laws or principles. (page 2)

Theory

A theory is not just a random thought or an unproven concept. Rather, a theory is an explanation of natural phenomena based on observation and accepted fundamental principles. To develop a physical theory, a physicist has to learn to ask appropriate questions, design experiments to try to answer the questions, and draw appropriate conclusions from the results. No theory is ever regarded as the final or ultimate truth. The possibility always exists that new observations will require that a theory be revised or discarded. It is in the nature of physical theory that we can disprove a theory by finding behavior that is inconsistent with it, but we can never prove that a theory is always correct. (page 2)

Range Of Validity

The extent to which a concept, conclusion, or measurement is well founded and corresponds accurately to the real world. (page 2)

I SEE

* Identify the relevent concept

* Set up the problem

* Execute the solution

* Evaluate your answer

Model/ Idealized Model

In everyday conversation we use the word "model" to mean either a small-scale replica or a person who displays articles of clothing (or the absence thereof). In physics a model is a simplified version of a physical system that would be too complicated to analyze in full detail. We have to overlook quite a few minor effects to make an idealized model, but we must be careful not to neglect too much. A useful model simplifies a problem enough to make it manageable, yet keeps its essential features. (page 3)

Point Object/ Particle

In physical science, a particle is a small localized object to which can be ascribed several physical or chemical properties such as volume, density, or mass. (page 3)

Physical Quantity

Any number that is used to describe a physical phenomenon quantitatively is called a physical quantity. In other cases we define a physical quantity by describing how to calculate it from other quantities that we can measure (e.g. average speed). (page 4)

Operational Definition

Some physical quantities are so fundamental that we can define them only by describing how to measure them. Such a definition is called an operational definition(e.g. distance by a ruler or time intervals by a stopwatch). (page 4)

Unit

When we measure a quantity, we always compare it with some reference standard. When we say that a Ferrari 458 Italia is 4.53 meters long, we mean that it is 4.53 times as long as a meter stick, which we define to be 1 meter long. Such a standard defines a unit of the quantity. When we use a number to describe a physical quantity, we must always specify the unit we are using; to describe a distance as simply "4.53" wouldn't mean anything.

"The Metric System"/ International System/ SI (Systeme International)

To make accurate, reliable measurements, we need units of measurement that do not change and can be duplicated by observers in various locations. The system of units by scientists and engineers around the world is commonly called the "the metric system," but since 1960 it has been known officially as the International System, or SI (the abbreviation for its French name, Systeme International). (page 4)

Second

Microwave radiation with a frequency of exactly 9,192,631,770 cycles per second causes the outermost electron of a cesium-133 electron to reverse its spin direction. An atomic clock uses this phenomenon to tune microwaves to this exact frequency. It then counts 1 second for each 9,192,631,770 cycles. One second (abbreviated s) is defined as the time required for this 9,192,631,770 cycles of this microwave radiation. (page 4)

Meter

The definition of a meter (abbreviated m) is the distance that light travels in a vacuum in 1/299,792,458 seconds. (page 5)

Kilogram

The standard of mass, the kilogram (abbreviated kg), is defined to be the mass of a particular cylinder of platinum-iridium alloy kept at the International Bureau of Weights and Measures at Sevres, near Paris. (page 5)

Derived Units

combinations of SI base units.

Fundamental Units

seven basic units of the SI measurement system: kilogram, second, mole, meter, ampere, Kelvin, candela.

British Units

These units are only used in the United States and a few other countries, and in most of these they are being replaced bu SI units. (page 6)

Dimensionally Consistent

We use equations to express relationships among physical quantities, represented by algebraic symbols. Each algebra symbol always denotes both a number and a unit. Equation in which every term has the same dimensions and the arguments of any mathematical functions appearing in the equation are dimensionless. (page 6)

Unit Multipliers

Becuase these fractions have units and are equal to 1 we call them Unit multipliers. (For example 1hr/60s.) (page 7)

Uncertainty/ Error

Measurements always have uncertainties. The uncertainty is also called the error because it indicates that maximum difference between there is likely to be between the measured value and the true value. (page 8)

Accuracy

We often indicate the accuracy of a measured value--that is how close it is likely to be to the true value--by writing the number, the symbol +-, and a second number indicating the uncertainty of the measurement. (For example, if the diameter of a steel rod is given an 56.47+-0.02mm, this means that the true value is likely to be within the range of 56.45 and 56.49.) In a commonly used short hand notation, the number 1.6454(21) means 1.6454+-0.0021. The number in the parenthesis shows the uncertainty in the final digits of the main number. (page 8)

Fractional/ Percent Error/Uncertaity

We can also express accuracy in terms of the maximum likely fractional error or percent error (also called fractional uncertainty or percent uncertainty). A resistor labeled "47 ohms +- 10%" probably has a true resistance the differs from 47 ohms by no more than 10% of 47 ohms. For the diameter of the steel rod above, the fractional error is (0.02mm)/(56.47), or about 0.0004; the percent error is (0.0004)(100%), or about 0.04%. Even small percent errors can be very significant. (page 8)

Significant Figures

In many cases the uncertainty of a number is not stated explicitly. Instead, the uncertainty is indicated by the number of meaningful digits, or significant figures, in the measured value. We gave the thickness of the cover of these books to be as 2.91 mm, which has three significant figures. Bu this we mean that the first few digits are known to be correct, while the third is uncertain. The last digit is in the hundredths place, so the uncertainty is about 0.01mm. Two values with the same number of significant figures may have different uncertainties. The zero to the left of a decimal place doesn't count. When you compute numbers that have uncertainties to compute other numbers, the computed numbers are also uncertain. When numbers are multiplied or divided, the result can have no more significant figures than the factor with the fewest significant figures has. When we add or subtract, the number of significant figures is determined by the term with the largest (i.e., fewest digits to the right of the decimal point). Always round your final answer to keep only the correct number of significant figures or, in doubtful cases, one more at most. Note that when you reduce the such an answer to the appropriate number of significant figures, you must round, not truncate. (page 9)

Scientific Notation/ Powers-Of-10 notation

When we work with very large or very small numbers, we can show significant figures much more easily by using scientific notation, sometimes called powers-of-10 notation. For example, 384,000,000m = 3.84*10^8m. (page9)

Note 1

When an integer or fraction occurs in an algebraic, we treat that number as having no uncertainty at all. (page 9)

Note 2

Precision is not the same as accuracy. (page 9)

Scalar Quatities

Some physical quantities, such as time, temperature, mass, and density, can be described completely by a single number and unit. When a physical quantity is described with a single number, we call it a scalar quantity. Quantities combining scalar quantities use the operation of ordinary arithmetic. (page 11)

Vector Quantity

Many other important quantities in physics have a direction associated with them and cannot be described with a single number. A vector quantity has both a magnitude and a direction in space. Combining of vectors requires a different set of operations. (page 11)

Magnitude

Greatness of size, strength, or importance. (page 11)

Displacement

Displacement is a change in the position of an object. Displacement is a vector quantity because we must state not only how far the object moves but also in what direction. (page 11)

Vector

We always draw a vector as a line with an arrowhead at it's tip. The length of the line shows the vector's magnitude, and the direction of the arrowhead shows the vector's direction. Displacement is always a straight-line segment directed from the staring point to the ending point, even though the object's actual path may be curved. Note that displacement is not directly related to the total distance traveled. (page 11)

Parallel

If two vectors have the same direction, they are parallel. (page 11)

Equal

If they have the same magnitude and the same direction, they are equal.