The nature around us is like a big chess game played by Nature. Various events that happen are like the moves made by a chess players. We are allowed to watch the events that happen, and guess the rules, and then play to derive benefits that we want from nature. We may across new events which do not follow old rules that we have formulated and we need to guess the new rules.
Great scientists or scientists in general guess the rules from the observations available at that time and prove the usefulness of those rules by further experiments or events that happen subsequently. These rules may require modification subsequently if they are not able to explain some events observed that happen subsequently.
Mathematics is the language of physics.
Units: Fundamental and derived
While there are a large number of physical quantities to be measured, only seven fundamental quantities are found to be sufficient. All other quantities can be measured using these seven fundamental quantities.
The set of fundamental quantities must have the following properties.
a. The fundamental quantities should be independent of each other; and
b. All other quantities may be expressed in terms of the fundamental quantities.
Fundamental quantities are also referred to as base quantities.
Who decides the units?
A body named Conference Generale des Poids or CGPM (General Conference on Weight and Measures in English) has been gibven the authority by international agreement.
Definition of base units
The distance travelled by light in vacuum in 1/[299,792,458] second is called 1 m.
the mass of cylinder made of planitum-iridium alloy kept at International Bureau of Weights and Measures is defined as 1 kg.
The time duration in 9,192,631,770 time periods of the selected transition of radiation of Cesium-133 atom is defined as 1 s. (To understand this idea see Bohr model chapter)
To under stand the definition of this unit, you have to read the chapter on electric field.
Two long straight wires with negligible cross section are to be placed parallel to each other at a separation of 1 m and electric current in the same amout is sent through them in the same direction. If the attractive force between the two wires adjusted, the current in each wire (one of the wires) that gives a force between them of 2*10^-7 newton per metre of the wires, is defined as 1 A of current.
The fraction 1/9273.16) of the thermodynamic temperature of triple point of water is called 1 K.
The amount of a substance that contain as many elementary entities (molecules or atoms if the substance is monatomic) as there are number of atoms in 0.012 kg of carbon-12 is called a mole.
It is the luminous intensity of a blackbody of surface area 1/[600,000] m² placed at the temperature of freezing platinum and at a pressure of 101,325 N/m², in the direction perpendicular to its surface.
Dimensions of physical quantities
When a physical quantity is expressed in terms of the base quantities, it is written as a product of different powers of the base quantities.
[Force] = MLT-2
M,L, and T are base quantities – mass, length and time
The exponent of a base quantity that enters into the expression (MLT-2) is called the dimension of the quantity in that base.
The dimensions or force are 1 in mass, 1 in length and -2 in time. The dimensions of all other base quantities are zero.
The base quantities are denoted as follows in writing expressions. The symbols used are M for mass, L of length, T for time, I for current, K for temperature, mol for mole and cd for candela.
The physical quantity that is expressed in terms of the base quantities is enclosed in square brackets to inform that it is expressed in dimensions of base quantities. Such expression of a physical quantity in terms of dimensions of base quantities is called the dimensional formula.
Order of magnitude
Convert the number into 1*10^c form.
First convert the number into a*10^b form in this case 1≤a<10 an="" and="" b="" br="" integer.="" is="">If a is less than or equal to 5 assume it is one and if a is greater than 5 assume it is 10 and convert the number into 1*10^c form.
Then c is the order of magnitude of the number.
The structure of the world
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