# 2011 in review

The WordPress.com stats helper monkeys prepared a 2011 annual report for this blog.

Here’s an excerpt:

The Louvre Museum has 8.5 million visitors per year. This blog was viewed about 78,000 times in 2011. If it were an exhibit at the Louvre Museum, it would take about 3 days for that many people to see it.

# Table of Units and Dimensions of Physical quantities.

Units & Dimensions of Physical quantities in S.I system.

Fundamental Physical Quantities:

 S.No Fundamental Physical Quantity Formula Dimensional Formula S.I Unit of physical quantity 1. Mass Amount of matter in the object M kg 2. Length L meter 3. Time T sec 4. Electric current I or A ampere 5. Amount of substance N mole(mol 6. Luminous intensity J candela(cd) 7. Temperature K or $\theta$ Kelvin

Derived Physical Quantities:

 S.No Derived Physical Quantity Formula Dimensional Formula S.I Unit of physical quantity 1. Area $l\times b$ [$latex{M^0L^2T^0}] $m^2$ 2. Volume $l\times b\times h$ [$M^0L^3T^o$] $m^3$ 3. Density $\frac{M}{V}$ [${M^1L^{-3}T^0$}] $kg/m^3$ 4. Specific Gravity $\frac{Density of Substance}{Density of Water}$ [$M^0L^0T^0$] No units 5. Frequency $\frac{no of vibrations}{Time}$ [$M^0L^0T^{-1}$] hertz 6. Angle $\frac{Arc}{radius}$ $M^0L^oT^o$ No units 7. Velocity $\frac{Displacement}{time}$ $M^0L^1T^{-1}$ m/sec 8. Speed $\frac{Distance}{time}$ $M^0L^1T^{-1}$ m/sec 9. Areal velocity $\frac{Area}{time}$ $M^0L^2T^{-1}$ $m^2sec^{-1}$ 10. Acceleration $\frac{Change in velocity }{time}$ $M^0L^1T^{-2}$ $m/sec^2$ 11. Linear momentum $M\times V$ $M^1L^1T^{-1}$ kg m/sec 12. Force $mass\times acceleration$ $M^1L^1T^{-2}$ kg-m/$sec^2$ or Newton 13. Weight w=mg $M^1L^1T^{-2}$ kg-m/$sec^2$ or Newton 14. Moment of force/Torque/Couple $Force\times arm$ $M^1L^2T^{-2}$ kg$m^2sec^{-2}$ 15. Impulse $Force\times time$ $M^1L^1T^{-1}$ kg m/sec or Ns 16. Pressure $\frac{Force}{Area}$ $M^1L^{-1}T^{-2}$ N/$m^2$ or Pa 17. Work $Force\times Distance$ $M^1L^2T^{-2}$ Nm or Joule 18. Kinetic Energy $\frac{1}{2} mv^2$ $M^1L^2T^{-2}$ joule 19. Potential Energy mgh $M^1L^2T^{-2}$ joule 20. Gravitational constant $\frac{Force\times (Length)^2}{(mass)^2}$ $M^{-1}L^3T^{-2}$ $kg^{-1}m^3sec^{-2}$ 21. Gravitational field strength $\frac{Force}{mass}$ $M^0L^1T^{-2}$ $N kg^{-1}$ 22. Gravitational Potential $\frac{Work}{mass}$ $M^0L^2T^{-2}$ $J kg^{-1}$ 23. Force constant (k) $\frac{F}{L}$ $M^1L^0T^{-2}$ $N m^{-1}$ 24. Power $\frac{Work}{time}$ $M^1L^2T^{-3}$ W or J/sec 25. Moment of Inertia ( I ) $Mass\times Distance^2$ $M^1L^2T^{0}$ kg$m^2$ 26. Stress $\frac{Force}{Area}$ $M^1L^{-1}T^{-2}$ N/$m^2$ or Pa 27. Strain $\frac{Change in length}{Origional length}$ $M^0L^0T^0$ No units 28. Modulus of Elasticity $\frac{Stress}{Strain}$ $M^1L^{-1}T^{-2}$ N/$m^2$ or Pa 29. Poission’s Ratio σ =$\frac{Y}{2n}$-1 $M^0L^0T^0$ No units 30. Velocity gradient $\frac{Change in velocity}{Distance}$ $M^0L^0T^{-1}$ $sec^{-1}$ 31. Coefficient of dynamic viscosity $\frac{Tangential stress}{Velocity Gradient}$ $M^1L^{-1}T^{-1}$ kg$m^{-1}sec^{-1}$(or) N-sec/$latex  \m^2$(or)pascal-sec (or)poiseuille 32. Surface Tension $\frac{Force}{Length}$ $M^1L^0T^{-2}$ $kg sec^2$,N/m 33. Angular displacement ($\theta$) $\frac{Arc}{radius}$ $M^0L^oT^o$ no Units 34. Angular velocity(ω) $\frac{Angular displacement}{Time}$ $M^0L^oT^{-1}$ rad/sec 35. Angular acceleration(α) $\frac{Change in angular velocity}{Time}$ $M^0L^oT^{-2}$ rad/$sec^{-2}$ 36. Angular momentum Iω $ML^2T^{-1}$ $kg-m^2 sec^{-1}$ 37. Angular Impulse Iω $ML^2T^{-1}$ $kg-m^2 sec^{-1}$ 38. Temperature $\theta$ or K kelvin or degree Celsius 39. Coefficient of linear expansion(α) $\frac{l_2-l_1}{l_1\times Temp(t_2-t_1)}$ $M^0L^0T^0K^{-1}$ /kelvin 40. Specific heat $\frac{Energy}{Mass\times Temp}$ $M^0L^2T^{-2}K^{-1}$ 41. Latent heat $\frac{Energy}{Mass}$ $M^0L^2T^{-2}$ $joule-kg^{-1}$ 42. Entropy $\frac{Q}\theta$ $M^1L^2T^{-2}K^{-1}$ $J K^{-1}$ 43. Thermal capacity $\frac{H}\theta$ $M^1L^2T^{-2}K^{-1}$ $J K^{-1}$ 44. Gas constant $\frac{PV}{m T}$ $M^0L^2T^{-2}K^{-1}$ $joule-K^{-1}$ 45. coefficient of thermal conductivity $\frac{Qd}{A(\theta_2-\Theta_1)t}$ $M^1L^1T^{-3}K^{-1}$ $W m^{-1}K^{-1}$ 46. Pole strength $Ampere\times meter$ $M^0L^1T^0I$ Am 47. Magnetic Moment $M^0L^2T^0I^1$ $Amp-m^2$ 48. Magnetic flux $\phi$ $ML^2T^{-2}I^{-1}$ weber ;$T-m^{2}$ ;J/Amp 49. Magnetic field,magnetic flux density (B) $MT^{-2}I^{-1}$ Tesla;$J/A-m^{2}$ 50. Permeability of free space $\frac{\mu}{\mu_r}$ $MLT^{-2}I^{-2}$ $NA^{-2}$ 51. Magnetic susceptibilty also called volumetric or bulk susceptibility χm χm = μr − 1 $M^0L^oT^o$ no units 52. Electric Charge $I\times T$ $M^0L^0T^1I^1$ Amp sec , coul 53. Electric potential $\frac{Work}{Charge}$ $M^1L^2T^{-3}I^{-1}$ Volt 54. E.M.F $\frac{Work}{Charge}$ $M^1L^2T^{-3}I^{-1}$ Volt 55. Electric Capacity $\frac{q}{V}$ $M^{-1}L^{-2}T^4I^2$ Farad 56. Electric Resistance $\frac{V}{i}$ $M^1L^2T^{-3}I^{-2}$ Ohm (Ω) or volt/amp 57. Resistivity $\rho$ $\frac{R A}{L}$ $M^1L^3T^{-3}I^{-1}$ Ohm mt (Ω-m) 58. Conductivity $\sigma$ 1/$\rho$ $M^{-1}L^{-3}T^3I$ Siemens/m 59. Permittivity $\varepsilon$ $M^{-1}L^{-3}T^4I^2$ farad/m 60. Electric conductance $\frac{1}{R}$ $M^{-1}L^{-2}T^3I^2$ Siemens (or) mhos 61. Electric power $V\times I$ $M^1L^2T^{-3}I^{-1}$ Watt 62. Electrical Impedance(Z) $\frac{V}{i}$ $M^1L^2T^{-3}I^{-2}$ Ohm (Ω) or volt/amp 63. Electrical admittance 1/Z(Reciprocal of electric impedance) $M^{-1}L^{-2}T^3I^3$ Siemens (or) mhos 64. Self Inductance(L) $\displaystyle v=L\frac{di}{dt}$ $ML^2T^{-2}I{-2}$ weber/amp or Henry 65. Boltzmann’s constant $\frac{Energy}{Temp}$ $M^1L^2T^{-2}K^{-1}$ J/kelvin 66. Stefan’s constant $\frac{E}{At \theta^4}$ $M^1L^0T^{-3}K^{-4}$ $W m^{-2}K^{-4}$ 67. Co-efficient of friction $\mu$ $\mu$=$\frac{F}{N}$,N=Normal reaction dimension less scalar no units 68. Dielectric constant $\varepsilon_r$ It is also called relative permittivity dimension less no units 69. Planck’s constant $E=h\nu$ $ML^2T^{-1}$ J.sec (or) eV.sec 70. Refractive index μ $M^0L^oT^o$ no units 71. Focal length(f) Distance between center of the lens(mirror) to its focus L meter 72. Power of a lens (P) The reciprocal of the focal length of a lens in meters is called power of a lens; p=1/f $L^{-1}$ diaptors 73. Wave number No.of waves/distance $L^{-1}$ $m^{-1}$ 74. Wave length Length of a wave L meter # Vector operations: Addition of vectors: If two scalars are added resulting scalar will be unique which will be equal to sum of the given two scalars.For examples if two scalars 2 and 8 are added their sum will be always equal to 2+8 =10. But, the addition of vectors is complicated.If we add two vectors of magnitudes 2 and 8 the resultant vector’s magnitude will be 6 or 10 or any value between 6 and 10 depending on the directions of the vectors we are adding. i) If the two given vectors are acting in same direction then the magnitude of the resultant vector will be 10 units, ii) If the two given vectors are acting in opposite directions then the magnitude of resultant vector will be 6 units, iii) If the two given vectors are acting in different directions then the magnitude of the resultant vector will be between 6 and 10. How to add two given vectors(Geometrical representation): Suppose $\overline{AB}$ and $\overline{CD}$ are two given vectors. i)If the two vectors are acting in the same direction,take the first vector Suppose $\overline{AB}$, to the terminal point of $\overline{AB}$ connect the initial point of $\overline{CD}$. We get $\overline{AB}$ + $\overline{CD}$ = $\overline{AD}$. The magnitude of resultant vector will be equal to the sum of magnitudes of $\overline{AB}$ and $\overline{CD}$ i.e When two vectors are acting in same direction thesum of the magnitudes of the vectors = Magnitude of resultant vector” AB+CD = AD ii)If the two vectors are acting in different directions in that case the procedure of addition will be same but the direction and magnitude of resultant vector will be different.Suppose $\overline{AB}$ and $\overline{CD}$ are two given vectors acting in different directions as shown in the below fig(a). To add these two vectors connect the initial point C of IInd vectors $\overline{CD}$ to the terminal point B of First vector $\overline{AB}$.Now join the initial point A of first vector $\overline{AB}$ with the terminal point D of the second vector $\overline{CD}$.The vector $\overline{AD}$ taken in reverse order $\overline{AD}$ (closing side taken in reverse order) represents the resultant vector both in magnitude and direction. I.e When two vectors are acting in different directions the “Sum of the magnitudes of the vectors > Magnitude of resultant vector”. Laws of vector addition: i) Vector addition is commutative $\bar{a}$ + $\bar{b}$ = $\bar{b}$$\bar{a}$ Proof:Suppose $\overline{OA}$ = $\bar{a}$ and $\overline{AB}$ = $\bar{b}$ are two given vectors.Now let us add these two vectors. To add them let us connect the initial position of $\overline{AB}$ to the terminal point of $\overline{OA}$ in anti clock wise direction,now closing side OB taken in the reverse order represents the resultant vector $\bar{r}$ . Now draw a vectors parallel to $\bar{a}$ and $\bar{b}$ and complete the parallelogram OABC.From the Fig(ii) $\overline{CB}$ = $\overline{OA}$ = $\bar{a}$ and $\overline{AB}$ = $\overline{OC}$ = $\bar{b}$. From triangle OAB $\overline{OA}$ + $\overline{AB}$ = $\overline{OB}$ i.e $\bar{a}$ + $\bar{b}$ = $\bar{r}$ – – – – – – – – – – – – (1) From triangle OCB $\overline{OC}$ + $\overline{CB}$ = $\overline{OB}$ i.e $\bar{b}$ + $\bar{a}$ = $\bar{r}$ – – – – – – – – – – – – (2) from eq(1) and (2) we get $\bar{a}$ + $\bar{b}$ = $\bar{b}$ + $\bar{a}$ Hence vector addition is commutative. ii) Vector addition is associative: Let $\overline{OA}$ = $\bar{a}$,$\overline{AB}$ = $\bar{b}$ and $\overline{BC}$ = $\bar{c}$ be three different vectors. To add the given three vectors $\bar{a}$ , $\bar{b}$ and $\bar{c}$ we have to connect the initial point of $\overline{AB}$ to the terminal point of $\overline{OA}$ and the initial point of $\overline{BC}$ to terminal point of $\overline{AB}$.The closing side taken in reverse order represents the resultant vector. Hence resultant $\overline{OC}$ = $\bar{r}$. Proof:To add three vectors we have to first add two vectors and to sum vector we will add the third vector. Form fig(ii) from the triangle OAB $\overline{OA}$ + $\overline{AB}$ =$\overline{OB}$ = ($\bar{a}$ + $\bar{b}$) – – – (1) from triangle OBC $\overline{OB}$ + $\overline{BC}$ = $\overline{OC}$ = $\bar{r}$ – – – – – – – – – – – – (2) substitute the value $\overline{BC}$ and $\overline{OB}$ = ($\bar{a}$ + $\bar{b}$) from eq(1) to eq(2) we get ($\bar{a}$ + $\bar{b}$) + $\bar{c}$ = $\overline{OC}$ = $\bar{r}$ – – – – – -(A) From triangle ABC $\overline{AB}$ + $\overline{BC}$ = $\overline{AC}$ i.e ($\bar{b}$ + $\bar{c}$) = $\overline{AC}$ – – – – – – – – – (3) From triangle OAC $\overline{OA}$ + $\overline{AC}$ = $\overline{OC}$ = $\bar{r}$ – – – – – – – – (4) solving eq(3) and eq(4) we get $\bar{a}$ + ($\bar{b}$ + $\bar{c}$) = $\overline{OC}$ = $\bar{r}$ – – – – – – – (B) Comparing eq(A) & eq(B) we get ($\bar{a}$ + $\bar{b}$) + $\bar{c}$ = $\bar{a}$ + ($\bar{b}$ + $\bar{c}$) Hence,vector addition is associative. Subtraction of Vectors: Subtraction of vectors is also a form of addition.Addition of two vectors acting in opposite direction is called subtraction of vectors. Suppose as in fig(i) $\overline{AB}$ = $\bar{a}$ and $\overline{CD}$ = $\bar{b}$ are two vectors, to subtract $\bar{b}$ from $\bar{a}$ we have to add the negative vector of $\bar{b}$ to $\bar{a}$, i.e $\bar{a}$$\bar{b}$ = $\bar{a}$ + ( –$\bar{b}$). In the fig (ii) we have drawn $\overline{BE}$ = (-$\bar{b}$) negative vector of $\overline{CD}$ = $\bar{b}$ , now connect the initial point of latex \overline{BE}$ to the terminal point of $\overline{AB}$. From the resultant vector of addition of these two vectors is $\overline{AE}$.

Therefore $\overline{AB}$ + $\overline{BE}$ = $\overline{AE}$

i.e $\bar{a}$ + (- $\bar{b}$) = $\bar{a}$$\bar{b}$ = $\overline{AE}$.

* Subtraction of vectors is not commutative  $\bar{a}$$\bar{b}$ $\not =$ $\bar{b}$$\bar{a}$

# HTML codes

{(X+Y+Z)
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 Posted in 5584 May·29 
 VECTORS Posted by gyaunnrraje 18 Physical quantities are classified in to two categories i) Scalar quantities ii)Vector quantities 1. Scalar quantities or Scalars :The physical quantities which have magnitude but no direction are called   scalar quantities or scalars. Ex:Length,mass,time,area,volume,speed,energy,work,temperature etc 2.Vector quantities or Vectors:The physical quantities which posses magnitude as well as direction are called Vector quantities or Vectors. Ex:Displacement,velocity,acceleration,momentum,force etc Geometrical representation of vectors :A vector is geometrically represented by a directed line segment. The length of the directed line segment is called magnitude of the vector and the direction of the line segment represents  the direction of the vector quantity.                                                   Ex: If a body starts from a point O after traveling for certain time it reaches its destination point A.Then the displacement of the body is represented by the directed line segment OA . The Length of the straight line OA represents the magnitude of the displacement of the body, and the direction of the line segment from O towards A represents the direction of displacement of the body. Vector $\overline{AB}$ is  read as AB bar.The magnitude of $\overline{AB}$ is written as $\mid$$\overline{AB}$$\mid$ and read as modulus of $\overline{AB}$. Types of Vectors : 1.Co-initial vectors: All those vectors whose initial points are same, such vectors are called co initial vectors.                                                                                                 Ex: OA,OB,OC, OD ,OE all these vectors have initial point O. Hence these are co-initial vectors. 2.Co-terminal vectors :All those vectors whose terminal (end) points are same,such vectors are     called co terminal vectors.                                                  Ex: The terminal point of all these vectors $\overline{AP}$,$\overline{BP}$,$\overline{CP}$ ,$\overline{DP}$   is Same  point P. Hence, these vectors are called co-terminal vectors. 3. Coplanar Vectors:The vectors which lie in the same plane  are called Co-planar  Vectors.   Ex:a) All the vectors which lie in XY plane are called coplanar irrespective of their magnitudes and  directions. b) all the vectors which lie in YZ plane are coplanar with respect to one another. 4.Null vectors: Any vector  which  has direction but no magnitude is called a null vector. For a null vector  its initial point  and the terminal point will be same . Ex: $\overline{AA}$ ,$\overline{BB}$ . $\overline{OO}$ ……………….   Are null vectors. 5.Unit Vector: Any vector of unit magnitude is called unit vector.If $\bar{a}$ is a vector,it’s unit vector is denoted by $\hat{a}$.This ($\hat{a}$) is read as a cap. If you divide a vector with its magnitude we get the unit vector of that vector. Therefore  unit vector  $\hat{a}= \frac{\bar{a}}{ \mid \bar{a} \mid}$ where $\mid \bar{a} \mid$ is called the magnitude of $\bar{a}$ vector. Every vector will have its own unit vector.Unit vector of any vector will be of unit magnitude irrespective of the magnitude of the original vector. If $\bar{b}$ is a vector its unit vector will be $\hat{b}$ ,the direction of $\bar{b}$ and $\hat{b}$ will be same.Similarly if $\bar{c}$ is a vector its unit vector will be $\hat{c}$ ,the direction of $\bar{c}$ and $\hat{c}$ will be same. Three mutually perpendicular axes OX,OY AND OZ form the Cartesian co-ordinate system.The unit vectors along X,Y and Z axis are represented by  $\hat{i}$ ,$\hat{j}$ and $\hat{k}$ respectively. 6.Like vectors : All the vectors acting in the same direction are called like vectors. The given vectors $\overline{AB}$ and $\overline{DC}$ are acting in the same direction ,hence $\overline{AB}$ and $\overline{DC}$ are like vectors. Note: Like vectors will be always i)parallel to one another ii) will be acting in the same direction , but iii)not necessarily be of the different  magnitudes. 7. Unlike Vectors : Any two vectors parallel to one another and acting in opposite directions are called unlike vectors. The given vectors $\overline{AB}$ and $\overline{CD}$are acting in the opposite directions , hence $\overline{AB}$ and $\overline{CD}$ are unlike  vectors. Note: Unlike vectors will be always i)parallel to one another ii) will be acting in the opposite directions , but iii)not necessarily be of the different  magnitudes. 8. Negative Vector : If $\overline{AB}$= $\bar{a}$ is a vector,then $\overline{DC}$ =  –$\bar{a}$ will be the negative vector of $\bar{a}$. i)The original vector $\bar{a}$ and it’s negative vector –$\bar{a}$ will be of same magnitude i.e $\mid \bar{a} \mid$ = $\mid \overline{-a} \mid$ ii) they will be opposite to one another. iii) every vector will have a negative vector. 9. Axial Vectors or (One dimensional Vectors) : The vectors acting along X,Y or Z axes ( or) vectors parallel to any one of the Axis are called axial vectors (or) one dimensional vectors. 9(i). Vectors parallel to X axis : In the Fig(1) all the vectors $\overline{AB}$ = $\bar{a}$ ,$\overline{CD}$ = $\bar{b}$ and $\overline{EF}$ = $\bar{c}$ are parallel to X axis. These vectors $\bar{a}$ , $\bar{b}$ and $\bar{c}$ are called axial vectors parallel to X-axis. If the magnitudes of vectors $\bar{a}$ , $\bar{b}$ and $\bar{c}$ are $\mid \bar{a} \mid$ =a ,$\mid \bar{b} \mid$ =b and ,$\mid \bar{c} \mid$ = c ,then we can represent the axial vectors as  $\bar{a}$ = a $\hat{i}$ ,  $\bar{b}$ = b $\hat{i}$ and $\bar{c}$ = c $\hat{i}$ . Ex: i)5 $\hat{i}$ is a vector of 5units magnitude working along X-axis or parallel to X-axis in positive direction. ii) 8/5  $\hat{i}$ is a vector of 8/5 units magnitude working along X-axis or parallel to X-axis in positive direction. iii) -9 $\hat{i}$ is a vector of 9units magnitude working along X-axis or parallel to X-axis in negative direction. iv)a $\hat{i}$ is a vector of a units magnitude working along X-axis or parallel to X-axis in positive direction. 9(ii). Vectors parallel to Y axis : In the Fig(2) all the vectors $\overline{AB}$ = $\bar{a}$ ,$\overline{CD}$ = $\bar{b}$ and  $\overline{EF}$ = $\bar{c}$ are parallel to Y axis. These vectors $\bar{a}$ , $\bar{b}$ and $\bar{c}$ are called axial vectors parallel to Y-axis. If the magnitudes of vectors $\bar{a}$ , $\bar{b}$ and $\bar{c}$ are $\mid \bar{a} \mid$ =a ,$\mid \bar{b} \mid$ =b and ,$\mid \bar{c} \mid$ = c ,then we can represent the axial vectors as  $\bar{a}$ = a $\hat{j}$ ,  $\bar{b}$ = b $\hat{j}$ and $\bar{c}$ = c $\hat{j}$ . Ex: i)3 $\hat{j}$ is a vector of 3units magnitude working along Y-axis or parallel to Y-axis in positive direction. ii) 5/3  $\hat{j}$ is a vector of 5/3units magnitude working along Y-axis or parallel to Y-axis in positive direction. iii) -7 $\hat{j}$ is a vector of 7units magnitude working along Y-axis or parallel to Y-axis in negative direction. iv)b $\hat{j}$ is a vector of b units magnitude working along Y-axis or parallel to Y-axis in positive direction. 9(iii). Vectors parallel to Z axis : In the Fig(3) all the vectors $\overline{AB}$ = $\bar{a}$ ,$\overline{CD}$ = $\bar{b}$ and  $\overline{EF}$ = $\bar{c}$ are parallel to Z axis. These vectors $\bar{a}$ , $\bar{b}$ and $\bar{c}$ are called axial vectors parallel to Z-axis. If the magnitudes of vectors $\bar{a}$ , $\bar{b}$ and $\bar{c}$ are $\mid \bar{a} \mid$ =a ,$\mid \bar{b} \mid$ =b and ,$\mid \bar{c} \mid$ = c ,then we can represent the axial vectors as  $\bar{a}$ = a $\hat{k}$ ,  $\bar{b}$ = b $\hat{k}$ and $\bar{c}$ = c $\hat{k}$ . Ex: i)6 $\hat{k}$ is a vector of 6units magnitude working along Z-axis or parallel to Z-axis in positive direction. ii) 8/5  $\hat{k}$ is a vector of 8/5 units magnitude working along Z-axis or parallel to Z-axis in positive direction. iii) -4 $\hat{k}$ is a vector of 4units magnitude working along Z-axis or parallel to Z-axis in negative direction. iv)c $\hat{k}$ is a vector of c units magnitude working along Z-axis or parallel to Z-axis in positive direction. 10.Two dimensional vectors (or) Plane vectors:The vectors acting in XY-Plane or YZ-Plane or ZX-Plane are known as two dimensional vectors or also known as vectors in a plane. 10(i).Vectors in XY-Plane: In the given Fig(i) $\overline{AB}$ = $\bar{a}$ is a vector working in XY-Plane.It’s X-component is $a_x$ $\hat{i}$ and Y component is $a_y$ $\hat{j}$.So we can express the given vector $\bar{a}$ as the sum of the component vectors. $\bar{a}$ = $a_x$ $\hat{i}$ + $a_y$ $\hat{j}$ . There fore the vectors acting in XY-Plane will have only two components X-component and Y-component.These XY-plane vectors can also be represented in Cartesian co-ordinate form. $\bar{a}$ =($a_x$ , $a_y$ , 0). Note: If X,Y co-ordinates exists(not equal to zero) and the Z co-ordinates does not exist(=0), such vectors will be in XY plane. 10(ii).Vectors in YZ-Plane:  In the given Fig(ii) $\overline{CD}$ = $\bar{a}$ is a vector working in YZ-Plane.It’s Y-component is $a_y$ $\hat{j}$ and Z component is $a_z$ $\hat{k}$.So we can express the given vector $\bar{a}$ as the sum of the component vectors. $\bar{a}$ = $a_y$ $\hat{j}$ + $a_z$ $\hat{k}$ . There fore the vectors acting in YZ-Plane will have only two components Y-component and Z-component.These YZ-plane vectors can also be represented in Cartesian co-ordinate form. $\bar{a}$ =(0,$a_y$ , $a_z$ ). Note: If Y,Z co-ordinates exists(not equal to zero) and the X co-ordinates does not exist(=0), such vectors will be in YZ plane. 10(iii).Vectors in XZ-Plane: In the given Fig(i) $\overline{EF}$ = $\bar{a}$ is a vector working in XZ-Plane.It’s X-component is $a_x$ $\hat{i}$ and Z component is $a_z$ $\hat{k}$.So we can express the given vector $\bar{a}$ as the sum of the component vectors. $\bar{a}$ = $a_x$ $\hat{i}$ + $a_z$ $\hat{k}$ . There fore the vectors acting in XZ-Plane will have only two components X-component and Z-component.These XZ-plane vectors can also be represented in Cartesian co-ordinate form. $\bar{a}$ =($a_x$ ,0, $a_z$ ). Note: If X,Z co-ordinates exists(not equal to zero) and the Y co-ordinates does not exist(=0), such vectors will be in XZ plane. 11.Space Vector: If any vector possess components along all the three  axes X,Y and Z such vectors are called space vectors. $\bar{a}$ = $a_x$ $\hat{i}$ + $a_y$ $\hat{j}$ + $a_z$ $\hat{k}$ .These space vectors can also be represented in Cartesian co-ordinate form. $\bar{a}$ =($a_x$ ,$a_y$, $a_z$ ). In the given fig $\overline{OE}$ is a space vector .Where OC =  $a_x$ , OA = $a_y$ and OG = $a_z$.Hence $\overline{OE}$ =  $\bar{r}$ =  $a_x$ $\hat{i}$ + $a_y$ $\hat{j}$ + $a_z$ $\hat{k}$ . Posted in Vectors Tagged Types of vectors May·17 Physics in Every Day Life Posted by gyaunnrraje 1 1.Does hot water put out a fire faster than cold water? Ans:Yes.When fire is caught if you sprinkle cold water,the water first absorbs heat from the flame and gets heated to boiling point.Then it absorbs heat further and becomes vapor.Once it is vaporized it occupies that region around the flame.Because of this,availability of oxygen around the flame will be reduced drastically and the fire will  put out. Instead of cold water if hot water is sprinkled it vaporizes faster than cold water hence the fire will put out faster in this case. 2.What is Heat? Ans:Heat is a form of energy,which gets transmitted between two bodies or two regions when they at at different temperatures.Heat always flows from a body at high temperature to a body at low temperature. Posted in Expansion of Gases, Expansion of Liquids, GENERAL, Physics in Every Day Life (Answers to common Questions) May·15 Types of Units Posted by gyaunnrraje 3 Generally we can use any convenient unit to measure a physical quantity depending on how much magnitude we are measuring or in which system of units we want to measure it. What kind of unit we should use? The unit i) must be accepted internationally. ii) Should be reproducible. iii) Should be invariable. iv) Should be easily available. v) Should be consistent. vi) Should be large, if the physical quantity to be measured is a big quantity. Ex: To measure larger lengths we use units like Km, mt etc, to measure large magnitude of time we use units like hour , day ,week, month , year etc. vii) Should be small if the physical quantity to be measured is small. Ex: To measure small time we use units like millisecond, microsecond etc To measure small lengths we use units like millimeter, centimeter etc. Types of physical Quantities.: We can broadly divide the physical quantities in to two types i)Fundamental Physical quantities ii)Derived physical quantities. Fundamental physical quantities: A physical quantity which can exist independently is called Fundamental physical quantity. Ex: Length, mass and time etc. Derived physical quantities: A physical quantity which can not exist independently is called derived physical quantity. (Or) A physical quantity which is dependent or derived from any other physical quantity is called derived physical quantity. Ex : Area, volume, density, speed, acceleration, force, energy etc. Like the physical quantities we can divide the units in to two types. I)Fundamental units ii)derived units. Fundamental units : The units of fundamental physical quantities are called fundamental units, (or) The units which are independent or can not derived from any other unit is called fundamental unit. Ex:­ Every unit of length is fundamental unit (irrespective of the system to which it belongs);millimeter, centimeter, meter, kilometer etc. ­ Every unit of time is a fundamental unit. microsecond, millisecond, second, minute, hour, day etc are units of time.All these units are fundamental units. Derived units: The units of derived physical quantities are called derived units. Units of area, volume, speed, density, energy etc are derived units. Ex: ­ Every unit of speed is a derived unit ; m/sec, cm/sec, km/hr etc. ­ Every unit of density is a derived unit; kg/m³, gr/cm³ etc. ­ Every unit of acceleration is a derived unit; m/sec², cm/sec², km/hr² etc. System of Units: To measure the fundamental physical quantities Length,Mass and Time we have three systems of units, they are i) C.G.S system(metric system) ii) F.P.S system (British system)   and iii) M.K.S system. In all these three systems only three physical quantities mass,length and time are considered to be fundamental quantities. But, in system International (S.I) system there are seven fundamental physical quantities. Which are i)Mass ii)Length iii) Time iv)Electric current v) Thermo dynamic temperature vi) Luminous intensity vii) Quantity of substance. In addition to the above seven fundamental quantities two more supplementary physical quantities were add.They are i) Plane angle ii)Solid angle. Posted in Physics Units Tagged system of units Apr·04 Post navigation ← Older posts