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Physicists observe the phenomena of nature and try to find patterns and principles thatrelate these phenomena. These patterns are called physical theories or, when they are very well

established and of broad use, physical laws or principles.(a theory is an explanation of natural phenomena based on observation and acceptedfundamental principles.)

Physics is based on experimental observations and quantitative measurements.The main objectives of physics are to identify a limited number of fundamental laws that governnatural phenomena and use them to develop theories that can predict the results of futureexperiments.1.1 Units & Standards

Whatever is chosen as a standard must be readily accessible and must possess someproperty that can be measured reliably. Measurement standards used by different people indifferent placesthroughout the Universemust yield the same result. In addition, standardsused for measurements must not change with time.

Some physical quantities are so fundamental that we can define them only bydescribing how to measure them. Such a definition is called an operational definition.The variables length, time, and mass are examples of fundamental quantities. Most

other variables are derived quantities, those that can be expressed as a mathematicalcombination of fundamental quantities. Common examples are area (a product of two lengths)and speed (a ratio of a length to a time interval). Another example of a derived quantity isdensity. The of any substance is defined as its mass per unit volume:

In 1960, an international committee established a set of standards for the fundamentalquantities of science. It is called the SI (Systme International), and its fundamental units oflength, mass, and time are the meter, kilogram, and second, respectively. Other standards forSI fundamental units established by the committee are those for temperature (the kelvin),electric current (the ampere), luminous intensity (the candela), and the amount of substance

(the mole).Length

We can identify length as the distance between two points in space. In October 1983,however, the meter was redefined as the distance traveled by light in vacuum during a timeof 1/299792458 second.

MassThe SI fundamental unit of mass, the kilogram (kg), is defined as the mass of a

specific platinumiridium alloy cylinder kept at the International Bureau of Weights andMeasures at Svres, France.

Time

One second is now defined as 9192631770 times the period of vibration of radiationfrom the cesium-133 atom.

The ampere is that constant currentwhich, ifmaintained in two straight parallelconductors of infinite length, of negligible circular cross-section, and placed 1metre apart invacuum, would produce between these conductors a force equal to 2 x 10 7newton per metreof length.

The kelvin, unit of thermodynamic temperature, is the fraction 1/273.16 of thethermodynamic temperature of the triple point of water.

The moleis the amount of substance of a system which contains as many elementaryentities as there are atoms in 0.012 kilogram of carbon 12.

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1. Physics & Measurement

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The candela is the luminous intensity, in a given direction, of a source that emitsmonochromatic radiation of frequency 540 x 1012 hertz and has a radiant intensity in thatdirection of (1/683) watt per steradian.

The supplementary SI units are two: the unit for (plane) angle, defined as the ratio of arclength to radius, is the radian(rad). For solid angle, defined as the ratio of the subtended areato the square of the radius, the unit is the steradian(sr).

Always Include Units When performing calculations with numerical values, include the units forevery quantity and carry the units through the entire calculation.

1.2 Model BuildingIn physics a model is a simplified version of a physical system that would be too

complicated to analyze in full detail. For example, suppose we want to analyze the motion of athrown baseball. How complicated is this problem? The ball is not a perfect sphere (it has raisedseams), and it spins as it moves through the air. Wind and air resistance influence its motion,the baIl's weight varies a little as its distance from the center of the earth changes, and so on. If

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we try to include all these things, the analysis gets hopelessly complicated. Instead, we invent asimplified version of the problem. We neglect the size and shape of the ball by representing it asa point object, or particle, We neglect air resistance by making the ball move in a vacuum, and

we make the weight constant. Now we have a problem that is simple enough to deal with

1.3 Dimensional Analysis

In physics, the word dimension denotes the physical nature of a quantity. The distancebetween two points, for example, can be measured in feet, meters, or furlongs, which are alldifferent ways of expressing the dimension of length.

In many situations, you may have to check a specific equation to see if it matches yourexpectations. A useful procedure for doing that, called dimensional analysis, can be usedbecause dimensions can be treated as algebraic quantities. For example, quantities can beadded or subtracted only if they have the same dimensions.

Any relationship can be correct only if the dimensions on both sides of the

equation are the same.

Questions1. (a) If an equation is dimensionally correct, does that mean that the equation must be true?

(b) If an equation is not dimensionally correct, does that mean that the equation cannot betrue?2. Which of the following equations are dimensionally correct? (a) vf= vi + ax (b) y = (2 m)cos(kx), where k =2 m-13. Newtons law of universal gravitation is represented by

where F is the magnitude of the gravitational force exerted by one small object on another, M

and m are the masses of the objects, and r is a distance. Force has the SI units kg.m/s2

. Whatare the SI units of the proportionality constant G?4. The position of a particle moving under uniform acceleration is some function of time and theacceleration. Suppose we write this position as x = kamtn, where k is a dimensionless constant.Show by dimensional analysis that this expression is satisfied if m = 1 and n = 2. Can thisanalysis give the value of k?5.( a) Assume the equation x =At3+ Bt describes the motion of a particular object, with x havingthe dimension of length and t having the dimension of time. Determine the dimensions of theconstants A and B.(b) Determine the dimensions of the derivative dx/dt = 3At2+ B.