Fundamentals of Physics/Physics and Measurement

The word Physics originates from the Greek word Physics, which means nature. Physics in raw terms is the study of everything around us. Physics is one of the oldest subjects (unknowing) invented by humanity. Possibly the oldest discipline in Physics could be astronomy.

Physicists try to express everyday happenings in concise mathematical formulas. These formulas are then used by other physicists and engineers to predict results of their experiments. For example, Isaac Newton (1642–1727) found the laws behind the motion of bodies, which we now use to design rockets that travel to the moon and other planets.

Physicists also revise the laws of physics from time to time according to experimental results. Isaac Newton found the laws of motion in the 17th century. These laws work at normal speeds, but when an object's speed approaches the speed of light, these laws fails. Albert Einstein (1879–1955) put forward the theory of relativity, which gives the same result as Newton's laws of motion at slow speeds, but is more accurate as speeds increase towards that of light.

Definition: "MEASUREMENT" is the determination of the size or magnitude of something. By comparing that unknown quantity with some standard quantity of equal nature, known as measurement unit. Measurement can also be defined as "Comparison of an unknown quantity with some known quantity of the same kind". Measurement of an object consists of: (1)- the unit of measurement. (2)- the number of units the object measures.

Measurement

Measurement is an integral part of Physics like any other scientific subject. Measurement is an integral part of human race, without it there will be no trade, no statistics. You can see the philosophy of measurement in the little kids who don't even know what math is. Kids try to compare their height, size of candy, size of dolls and amount of toys they have. All these happen even before they know math. Math is built into our brains even before we start to learn it. Math provides a great way to study about anything, that's why we see computers involved in almost anything because they are good at math.

Scale

Scales are used to measure. One would know a simple ruler or tape could be used to measure small distances, your height, and possibly much more. In Physics, we do have certain scales for certain quantities which we will see very shortly. Scale is the ratio between the actual distance on the ground and the distance shown on the map. - The distance between the school and the home of a student is 10 km. If he shows this 10 km distance by 2 cm on the map, it means, 1cm on the map will show 5km on the ground.

The four types of scales are: Nominal Scale. Ordinal Scale. Interval Scale. Ratio Scale.

Length, Mass and Time

The current system of units has three standard units: the meter, kilogram, and second. These three units form the mks-system or the metric system.

A meter is a unit of length, currently defined as the distance that light travels in 1/299,792,458 of a second.

A kilogram is a unit of mass. While it was previously defined as a specific volume of water (i.e. 1 liter or a 10 cm³ cube), its current definition is based on a prototype platinum-iridium cylinder.

A second is a unit of time. Originally defined as the amount of time the earth needs to make 1/86,400 of a rotation, it is now defined as 9,192,631,770 oscillations of a cesium-133 atom.

Dimensional and Unit Analysis

Dimensional analysis is used to determine if an equation is dimensionally correct. When you are presented with an equation, dimensional analysis is performed by stripping the numerical components and leaving only the unit types (length, mass, or time). It may also be used to determine the type of unit used for an unknown variable. For example, the force of gravity may appear as the following:

${\text{weight force (weight)}}=9.8m/s^{2}*{\text{mass}}$

It gets converted to the following:

${\text{unbalanced force}}={\frac {\text{length}}{\text{time}}}*{\text{mass}}$

and as such, the unit of force involves multiplying length and mass, and dividing by the square of the time.

Unit analysis is similar to dimensional analysis, except that it uses units instead of the basic dimensions. The same principle applies; the numbers are removed, and the units are verified to be equal on both sides of the equation.

Density Formula

The formula for density is Density Formula

d = density m = mass v = volume

Density

Density is the amount of mass per volume, or the quantity of mass per unit volume of a substance. The density (or more precisely, the volumetric mass density) of a substance is its mass per unit volume. The symbol most often used for density is ρ (the lower case Greek letter rho). Mathematically, density is defined as mass divided by volume:[1]

$\rho ={\frac {m}{V}},$

where ρ is the density, m is the mass, and V is the volume. In some cases (for instance, in the United States oil and gas industry), density is loosely defined as its weight per unit volume,[2] although this is scientifically inaccurate – this quantity is more properly called specific weight.

In a pure substance, the density has the same numerical value as its mass concentration. Different materials usually have different densities, and density may be relative to buoyancy, purity and packaging. Osmium and iridium are the densest known elements at standard conditions for temperature and pressure, but certain chemical compounds may be denser.

To simplify comparisons of density across different systems of units, it is sometimes replaced by the dimensionless quantity "relative density" or "specific gravity", i.e. the ratio of the density of the material to that of a standard material, usually water. Thus a relative density less than one means that the substance floats in water.

The density of a material varies with temperature and pressure. This variation is typically small for solids and liquids but much greater for gases. Increasing the pressure on an object decreases the volume of the object and thus increases its density. Increasing the temperature of a substance (with a few exceptions) decreases its density by increasing its volume. In most materials, heating the bottom of a fluid results in convection of the heat from the bottom to the top, due to the decrease in the density of the heated fluid. This causes it to rise relative to more dense unheated material.

The reciprocal of the density of a substance is occasionally called its specific volume, a term sometimes used in thermodynamics. Density is an intensive property in that increasing the amount of a substance does not increase its density; rather it increases its mass.

Conversion of Units

How many kilometers are in 20 miles? To find out, you have to convert the miles into kilometers.

A conversion factor is a ratio between two compatible units.

$20{\text{ miles}}=20{\text{ miles}}*{\frac {1{\text{ km}}}{0.621{\text{ miles}}}}=32.2{\text{ km}}$

You may also see conversion factors for weight and mass (e.g. pounds and kilograms). These factors rely on equivalence (e.g. 1 kilogram is "close enough" to 2.2 pounds) based on external factors. While that cannot apply in all situations, these factors may be used in some limited scopes.

Estimates and Order-of-Magnitude calculation

The order of magnitude gives the approximate idea of the powers of 10 .Any number in the form a*10b [ here a multiplied by 10.. And 10raised to the power b]if a >or = (10)^0.5 the a become 1 and b is not changed but when a>(10)^0.5 then a is taken as 10 so power of b increases by 1. This results in order of magnitude calculation

Significant Figures

A significant figure is a digit within a number that is expected to be accurate. In contrast, a doubtful figure is a digit that might not be correct. Significant figures are relevant in measured numbers, general estimates or rounded numbers.

As a general rule, any non-zero digit shown is a significant figure. Zeros that appear after the decimal point and are at the end of the number are also significant. Zeros at the end of the number but before the decimal point are not included as significant figures (although exceptions may occur.)

In general, an operation performed on two numbers will result in a new number. This new number should have the same number of significant digits as the least accurate number. If an exact number is used, it should have the same number of digits as the estimated number. If both numbers are exact, the new number should be calculated fully (within reason).

When doing calculations, you should only keep at most 1 doubtful digit; while it is acceptable to keep them when using a handheld calculator or computer, the final answer should be adjusted to reflect the correct number of significant digits.

Other units

The current metric system also includes the following units:

• An ampere (A) is a measure for electric current.
• A kelvin (K) is a measure for temperature.
• A mole (mol) is the amount of substance (based on number of atoms rather than mass.)
• A candela (cd) is a measure for luminous intensity.
• The Lumen (lm) is a measure unit for total amount light visible for the human eye emitted by a source.
• The lux (lx) is a measure unit for luminous flux per unit area.

Slug

A slug is a unit of mass in the FPS (foot-pound-second) system. It is defined as the force required to accelerate 1 pound of mass to 1 ft/s², where 1 pound (lb) is equal to 456 grams. Thus a slug in equal to 14.5 kilograms, or 32.174 pounds. In the FPS system, one pound is the equivalent of 4.45 Newtons. Note: A slug is also an animal similar to a snail.