# Measurement Units And Dimensions In Physics Pdf Mechanics

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Published: 15.04.2021  Figure 1. The distance from Earth to the Moon may seem immense, but it is just a tiny fraction of the distances from Earth to other celestial bodies.

The thumbnail image is of the Whirlpool Galaxy, which we examine in the first section of this chapter. Galaxies are as immense as atoms are small, yet the same laws of physics describe both, along with all the rest of nature—an indication of the underlying unity in the universe. In this text, you learn about the laws of physics.

Figure 1. The distance from Earth to the Moon may seem immense, but it is just a tiny fraction of the distances from Earth to other celestial bodies. We define a physical quantity either by specifying how it is measured or by stating how it is calculated from other measurements.

For example, we define distance and time by specifying methods for measuring them, whereas we define average speed by stating that it is calculated as distance traveled divided by time of travel. Measurements of physical quantities are expressed in terms of units , which are standardized values. For example, the length of a race, which is a physical quantity, can be expressed in units of meters for sprinters or kilometers for distance runners.

Without standardized units, it would be extremely difficult for scientists to express and compare measured values in a meaningful way. See Figure 2. There are two major systems of units used in the world: SI units also known as the metric system and English units also known as the customary or imperial system. English units were historically used in nations once ruled by the British Empire and are still widely used in the United States.

Virtually every other country in the world now uses SI units as the standard; the metric system is also the standard system agreed upon by scientists and mathematicians.

Table 1 gives the fundamental SI units that are used throughout this textbook. This text uses non-SI units in a few applications where they are in very common use, such as the measurement of blood pressure in millimeters of mercury mm Hg.

Whenever non-SI units are discussed, they will be tied to SI units through conversions. It is an intriguing fact that some physical quantities are more fundamental than others and that the most fundamental physical quantities can be defined only in terms of the procedure used to measure them.

The units in which they are measured are thus called fundamental units. In this textbook, the fundamental physical quantities are taken to be length, mass, time, and electric current. Note that electric current will not be introduced until much later in this text. All other physical quantities, such as force and electric charge, can be expressed as algebraic combinations of length, mass, time, and current for example, speed is length divided by time ; these units are called derived units.

The SI unit for time, the second abbreviated s , has a long history. Cesium atoms can be made to vibrate in a very steady way, and these vibrations can be readily observed and counted. In the second was redefined as the time required for 9,,, of these vibrations.

See Figure 3. Accuracy in the fundamental units is essential, because all measurements are ultimately expressed in terms of fundamental units and can be no more accurate than are the fundamental units themselves.

Figure 3. An atomic clock such as this one uses the vibrations of cesium atoms to keep time to a precision of better than a microsecond per year. The fundamental unit of time, the second, is based on such clocks.

This image is looking down from the top of an atomic fountain nearly 30 feet tall! The SI unit for length is the meter abbreviated m ; its definition has also changed over time to become more accurate and precise.

This measurement was improved in by redefining the meter to be the distance between two engraved lines on a platinum-iridium bar now kept near Paris. By , it had become possible to define the meter even more accurately in terms of the wavelength of light, so it was again redefined as 1,, See Figure 4. This change defines the speed of light to be exactly ,, meters per second.

The length of the meter will change if the speed of light is someday measured with greater accuracy. The SI unit for mass is the kilogram abbreviated kg ; it is defined to be the mass of a platinum-iridium cylinder kept with the old meter standard at the International Bureau of Weights and Measures near Paris.

The determination of all other masses can be ultimately traced to a comparison with the standard mass. Figure 4. Distance traveled is speed multiplied by time. The initial modules in this textbook are concerned with mechanics, fluids, heat, and waves. In these subjects all pertinent physical quantities can be expressed in terms of the fundamental units of length, mass, and time.

SI units are part of the metric system. The metric system is convenient for scientific and engineering calculations because the units are categorized by factors of Table 2 gives metric prefixes and symbols used to denote various factors of Metric systems have the advantage that conversions of units involve only powers of There are centimeters in a meter, meters in a kilometer, and so on.

In non-metric systems, such as the system of U. Another advantage of the metric system is that the same unit can be used over extremely large ranges of values simply by using an appropriate metric prefix.

For example, distances in meters are suitable in construction, while distances in kilometers are appropriate for air travel, and the tiny measure of nanometers are convenient in optical design. With the metric system there is no need to invent new units for particular applications. The term order of magnitude refers to the scale of a value expressed in the metric system.

Order of magnitude can be thought of as a ballpark estimate for the scale of a value. The diameter of an atom is on the order of 10 -9 m while the diameter of the Sun is on the order of 10 9 m. The fundamental units described in this chapter are those that produce the greatest accuracy and precision in measurement. There is a sense among physicists that, because there is an underlying microscopic substructure to matter, it would be most satisfying to base our standards of measurement on microscopic objects and fundamental physical phenomena such as the speed of light.

A microscopic standard has been accomplished for the standard of time, which is based on the oscillations of the cesium atom. The standard for length was once based on the wavelength of light a small-scale length emitted by a certain type of atom, but it has been supplanted by the more precise measurement of the speed of light.

If it becomes possible to measure the mass of atoms or a particular arrangement of atoms such as a silicon sphere to greater precision than the kilogram standard, it may become possible to base mass measurements on the small scale. There are also possibilities that electrical phenomena on the small scale may someday allow us to base a unit of charge on the charge of electrons and protons, but at present current and charge are related to large-scale currents and forces between wires.

The vastness of the universe and the breadth over which physics applies are illustrated by the wide range of examples of known lengths, masses, and times in Table 1.

Examination of this table will give you some feeling for the range of possible topics and numerical values. See Figure 5 and Figure 6. Figure 5. Tiny phytoplankton swims among crystals of ice in the Antarctic Sea.

They range from a few micrometers to as much as 2 millimeters in length. Gordon T. Figure 6. Galaxies collide 2. The tremendous range of observable phenomena in nature challenges the imagination. Mahdavi et al. Hoekstra et al. It is often necessary to convert from one type of unit to another. For example, if you are reading a European cookbook, some quantities may be expressed in units of liters and you need to convert them to cups. Or, perhaps you are reading walking directions from one location to another and you are interested in how many miles you will be walking.

In this case, you will need to convert units of feet to miles. Let us consider a simple example of how to convert units. Let us say that we want to convert 80 meters m to kilometers km. The first thing to do is to list the units that you have and the units that you want to convert to. In this case, we have units in meters and we want to convert to kilometers. Next, we need to determine a conversion factor relating meters to kilometers.

A conversion factor is a ratio expressing how many of one unit are equal to another unit. For example, there are 12 inches in 1 foot, centimeters in 1 meter, 60 seconds in 1 minute, and so on. In this case, we know that there are 1, meters in 1 kilometer.

Now we can set up our unit conversion. We will write the units that we have and then multiply them by the conversion factor so that the units cancel out, as shown:. Note that the unwanted m unit cancels, leaving only the desired km unit. You can use this method to convert between any types of unit. Suppose that you drive the Note: Average speed is distance traveled divided by time of travel.

First we calculate the average speed using the given units. Then we can get the average speed into the desired units by picking the correct conversion factor and multiplying by it. The correct conversion factor is the one that cancels the unwanted unit and leaves the desired unit in its place. Average speed is distance traveled divided by time of travel. Take this definition as a given for now—average speed and other motion concepts will be covered in a later module.

In equation form,. If you have written the unit conversion factor upside down, the units will not cancel properly in the equation. If you accidentally get the ratio upside down, then the units will not cancel; rather, they will give you the wrong units as follows:.

Because each of the values given in the problem has three significant figures, the answer should also have three significant figures. The answer Note that the significant figures in the conversion factor are not relevant because an hour is defined to be 60 minutes, so the precision of the conversion factor is perfect. ## Dimensional analysis

In engineering and science , dimensional analysis is the analysis of the relationships between different physical quantities by identifying their base quantities such as length , mass , time , and electric charge and units of measure such as miles vs. The conversion of units from one dimensional unit to another is often easier within the metric or SI system than in others, due to the regular base in all units. Dimensional analysis, or more specifically the factor-label method , also known as the unit-factor method , is a widely used technique for such conversions using the rules of algebra. Commensurable physical quantities are of the same kind and have the same dimension, and can be directly compared to each other, even if they are originally expressed in differing units of measure, e. Incommensurable physical quantities are of different kinds and have different dimensions, and can not be directly compared to each other, no matter what units they are originally expressed in, e. It is must to measure all Physical quantities so that we can use them. In this chapter we the dimension and dependence of the unit of any Physical quantity on fundamental quantities or unit. derive formula if in mechanics a physical quantity.

## Section Summary

In this article, we shall study the concept of dimensions of physical quantities and to find dimensions of given physical quantity. Dimensions of Physical Quantity:. The power to which fundamental units are raised in order to obtain the unit of a physical quantity is called the dimensions of that physical quantity. Dimensions of physical quantity do not depend on the system of units.

Physics is a quantitative science, based on measurement of physical quantities. Certain physical quantities have been chosen as fundamental or base quantities. The fundamental quantities that are chosen are Length, Mass, Time, electric current, thermodynamic temperature, amount of substance, and luminous intensity. Each base quantity is defined in terms of a certain basic arbitrarily chosenbut properly standardised reference standard called unit such as metre,kilogram,second,ampere,kelvin,mole,and candela.

A physical quantity is a property of a material or system that can be quantified by measurement. A physical quantity can be expressed as the combination of a numerical value and a unit. For example, the physical quantity mass can be quantified as n kg , where n is the numerical value and kg is the unit. A physical quantity possesses at least two characteristics in common, one is numerical magnitude and other is the unit in which it is measured. #### Physical Quantities and Units

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Physicists, like other scientists, make observations and ask basic questions.