physics-class-11-unit-02-chapter-01-units-of-measurement-si-units-fundamental-lecture-1-4-4j-u4c-nlza

### <Success style="font-size:25px"> Units Of Measurement Si Units Fundamental L-1 </Success>
### <primary style="font-size:24px"> Units and Measurements </primary>
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* Units- Fundamental and derived units.
 
* Different systems of units - SI units.

* Measurement of length mass and time range of measurement for these quantities.

* We start by learning how to measure physical quantities.

* Length, Mass, Time, Temperature, Force, Pressure, Speed.

* We define a physical quantity by setting up a standard and assigning a unit to that standard For eg. we assign a specific length,say it is 1 metre.

* Now any other length is expressed as a multiple of this length. Something which is twice as long as the standard length 2m as small as radius of a hydrogen atom or as large as distance from moon to earth.

* Standard length <math xmlns="http://www.w3.org/1998/Math/MathML"> <mstyle displaystyle="true"> <mo>→</mo> </mstyle> </math> Unit Length.

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<footer style = "font-size: 18px"> $\rightarrow$ Units of Measurement,SI Units Fundamental $\rightarrow$ <span style = "color:blue"> Units and Measurements </span> $\rightarrow$ Physical Quantity $\rightarrow$ Different Units of Measurement </footer>

### <Success style="font-size:25px"> Units Of Measurement Si Units Fundamental L-1 </Success>
### <primary style="font-size:24px"> Physical Quantity </primary>
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- Physical Quantity Q = n x u

-  n <math xmlns="http://www.w3.org/1998/Math/MathML"> <mstyle displaystyle="true"> <mo>→</mo> </mstyle> </math> Magnitude of the quantity.

-  u <math xmlns="http://www.w3.org/1998/Math/MathML"> <mstyle displaystyle="true"> <mo>→</mo> </mstyle> </math> Unit.
 
- The same quantity can be expressed in different sets of unit.

* A large number of physical quantities
- (eg. length, area, vollume, speed, acceleration, mass, force, time...).
- We require only a few quantities which are independent and the other (dependent) quanties can be expressed in terms of these independent quantities.

* Independent quantities - Fundamental units, Other quantities - Derived units.
* Derived quantities are obtained by multiplication or division of powers of fundamental quantities.
* Complete set of units (both basic and derivel quantities) - System of units.

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<footer style = "font-size: 18px">Units of Measurement,SI Units Fundamental $\rightarrow$ Units and Measurements $\rightarrow$ <span style = "color:blue"> Physical Quantity </span> $\rightarrow$ Different Units of Measurement $\rightarrow$ Different Units of Measurement </footer>

### <Success style="font-size:25px"> Units Of Measurement Si Units Fundamental L-1 </Success>
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- **Till 1970's 3 Major Systems**

- **a) CGS System of Units**

* Centimetre used for length.
* Gram used for mass.
* Second used for time.

- **b) FPS System**
* Foot was used for length.
* Pound was used for mass.
* Second was used for time.

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<footer style = "font-size: 18px">Units and Measurements $\rightarrow$ Physical Quantity $\rightarrow$ <span style = "color:blue"> Different Units of Measurement </span> $\rightarrow$ Different Units of Measurement $\rightarrow$ International System of Units </footer>

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- **c) MKS System**

* Metre was used for length.
* Kilogram used for mass.
* Second used for time.

- System of units <math xmlns="http://www.w3.org/1998/Math/MathML"> <mstyle displaystyle="true"> <mo>→</mo> </mstyle> </math> Standardized
-  SI units (System International units) <math xmlns="http://www.w3.org/1998/Math/MathML"> <mstyle displaystyle="true"> <mo>→</mo> </mstyle> </math>
-  based on decimal system
- SI units <math xmlns="http://www.w3.org/1998/Math/MathML"> <mstyle displaystyle="true"> <mo>→</mo> </mstyle> </math> Seven base units used.

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<footer style = "font-size: 18px">Physical Quantity $\rightarrow$ Different Units of Measurement $\rightarrow$ <span style = "color:blue"> Different Units of Measurement </span> $\rightarrow$ International System of Units $\rightarrow$ Radian and Steradian </footer>

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### <primary style="font-size:24px"> International System of Units </primary>
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| Length| Metre | m |
|---|---|---|
| Mass | kilogram | kg |
| Time | Second | s |
| Electric current| Ampere | A |
| Temperature | Kelvin | K |
| Amount of Substance | Mole | mol |
| Luminous Intensity | Candela | cd |

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- **1) Planar Case Radian**

- <math xmlns="http://www.w3.org/1998/Math/MathML"> <mstyle displaystyle="true"> <mo>Θ</mo> </mstyle> </math> = <math xmlns="http://www.w3.org/1998/Math/MathML"> <mstyle displaystyle="true"> <mfrac> <mi>S</mi> <mi>r</mi> </mfrac> </mstyle> </math>    in radians

- <math xmlns="http://www.w3.org/1998/Math/MathML"> <mstyle displaystyle="true"> <mfrac> <mrow> <mn>2</mn> <mi>π</mi> <mi>r</mi> </mrow> <mi>r</mi> </mfrac> <mo>=</mo> <mn>2</mn> <mi>π</mi> </mstyle> </math> radians

- <math xmlns="http://www.w3.org/1998/Math/MathML"> <mstyle displaystyle="true"> <mfrac> <mi>S</mi> <mi>r</mi> </mfrac> </mstyle> </math> radians = <math xmlns="http://www.w3.org/1998/Math/MathML"> <mstyle displaystyle="true"> <msup> <mn>360</mn> <mo>∘</mo> </msup> </mstyle> </math>

- $1^{\circ} = \frac{2\pi}{360} \text{radians} $

- $= \frac{\pi}{180} \text{radians}$

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- **2) Steradian**

- <math xmlns="http://www.w3.org/1998/Math/MathML"> <mstyle displaystyle="true"> <mi>d</mi> <mo>Ω</mo> </mstyle> </math>

- <math xmlns="http://www.w3.org/1998/Math/MathML"> <mstyle displaystyle="true"> <mfrac> <mrow> <mi>d</mi> <mi>A</mi> </mrow> <msup> <mi>r</mi> <mn>2</mn> </msup> </mfrac> <mo>=</mo> <mi>d</mi> <mo>Ω</mo> </mstyle> </math>  (in steradian)

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<footer style = "font-size: 18px">International System of Units $\rightarrow$ Radian and Steradian $\rightarrow$ <span style = "color:blue"> Radian and Steradian </span> $\rightarrow$ Different Units $\rightarrow$ SI Prefixes </footer>

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-  1 minute = 60s
 
-  1 hour = 60min = 3600s

- 1 day = 86400 sec

- Angle <math xmlns="http://www.w3.org/1998/Math/MathML"> <mstyle displaystyle="true"> <mo>→</mo> </mstyle> </math> radian

- Also measured in degrees.

- Light year <math xmlns="http://www.w3.org/1998/Math/MathML"> <mstyle displaystyle="true"> <mo>→</mo> </mstyle> </math> distance travelled by light in 1 year.

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<footer style = "font-size: 18px">Radian and Steradian $\rightarrow$ Radian and Steradian $\rightarrow$ <span style = "color:blue"> Different Units </span> $\rightarrow$ SI Prefixes $\rightarrow$ SI Prefixes </footer>

### <Success style="font-size:25px"> Units Of Measurement Si Units Fundamental L-1 </Success>
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| Multiply | Prefix   |
| -------- | -------- |
| $10^3$    | kilo     |
| $10^6$    | mega     |
| $10^9$    | giga     |
| $10^{12}$ | tera     |
| $10^{15}$ | peta     |

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<footer style = "font-size: 18px">Radian and Steradian $\rightarrow$ Different Units $\rightarrow$ <span style = "color:blue"> SI Prefixes </span> $\rightarrow$ SI Prefixes $\rightarrow$ Measurement of Length</div> </footer>

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- Direct measurement of length - metre scale range of <math xmlns="http://www.w3.org/1998/Math/MathML"> <mstyle displaystyle="true"> <msup> <mn>10</mn> <mn>-3</mn> </msup> </mstyle> </math> to <math xmlns="http://www.w3.org/1998/Math/MathML"> <mstyle displaystyle="true"> <msup> <mn>10</mn> <mn>-2</mn> </msup> </mstyle> </math> m.

- Vernier Calliper $\sim 10^{-4}$ m

- Micrometer screw guage $\sim 10^{-5}$ m

- **Large distances  - Parallax method.**

- Large distances are measured by method of parallax..

- When the same point is observed by two different observation points, it seems that position of the point has changed. This shift is called parallax.

- This shift <math xmlns="http://www.w3.org/1998/Math/MathML"> <mstyle displaystyle="true"> <mo>→</mo> </mstyle> </math> </math> PARALLAX

- The distance between the 2 observation points <math xmlns="http://www.w3.org/1998/Math/MathML"> <mstyle displaystyle="true"> <mo>→</mo> </mstyle> </math> </math> basis (b)

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<footer style = "font-size: 18px">SI Prefixes $\rightarrow$ SI Prefixes $\rightarrow$ <span style = "color:blue"> Measurement of Length</div> </span> $\rightarrow$ Parallax Method $\rightarrow$ Parallax Method </footer>

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- Distance from  S to A  or S to B is given by D.

- Distance between A & B (basis) = b

- Measure the angle between the two directions along when S is viewed.

- If $\frac{b}{D} << 1$, angle $\theta$ will be small.

- AB - treated as one of the circle.

- If we want to measure the size or angular diameter of a planet.

- Angle subtended by the 2 opposite points = $\alpha$.

- Diametrically opposite on the planet.

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<footer style = "font-size: 18px">SI Prefixes $\rightarrow$ Measurement of Length</div> $\rightarrow$ <span style = "color:blue"> Parallax Method </span> $\rightarrow$ Parallax Method $\rightarrow$ Parallax Method </footer>

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- If distance of planet from earth $=D$

- $ d=\alpha D \Rightarrow \alpha=\frac{d}{D} $

- $1 \text { degree }=\frac{\pi}{180} \mathrm{rad}=1.745 \times 10^{-2} \mathrm{rad}$

- $ 1 \text { degree }=60 \text { minutes }$

- $1 \text { minute or } 1^{\prime}=\frac{1}{60^{\circ}}=\frac{1.745 \times 10^{-2}}{60} \mathrm{rad}$

- $1 \mathrm{sec}=\frac{1}{60} \min =1^{\prime \prime}=\frac{1.745 \times 10^{-2}}{60 \times 60} \mathrm{rad}$

- Moon is observed from 2 diametrically opposite points on the earth.

- Angle suspended by the 2 line of observation.

- $1^{\circ} 54^{\prime}$

- Diameter of earth = $1.276 \times 10^7$

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<footer style = "font-size: 18px">Measurement of Length</div> $\rightarrow$ Parallax Method $\rightarrow$ <span style = "color:blue"> Parallax Method </span> $\rightarrow$ Parallax Method $\rightarrow$ Parallax Method </footer>

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- Moon is observed from 2 diametrically opposite points on the earth.

- Angle suspended by the 2 line of observation.

- $1^{\circ} 54^{\prime}$

- Diameter of earth = $1.276 \times 10^7$

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<footer style = "font-size: 18px">Parallax Method $\rightarrow$ Parallax Method $\rightarrow$ <span style = "color:blue"> Parallax Method </span> $\rightarrow$ Parallax Method $\rightarrow$ Thank You </footer>

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- Find the distance between earth and moon.

- $A B=$ Diameter of earth $=D \theta$

- $\theta \rightarrow$ Convert to radians

- $1^{\circ} 54^{\prime} \rightarrow$ radians $\rightarrow 60^{\prime}+54^{\prime}=114^{\prime}$

- $\ 1.276 \times 10^7 \mathrm{m}=D \times 114 \times \frac{1.745 \times 10^{-2}}{60}$

- $D=\frac{1.276 \times 10^7 \times 60}{114 \times 1.745 \times 10^{-2}} \mathrm{m}$

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