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Unit And Dimension

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Published in: Physics
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Powerpoint presentation upon Unit and Dimension. This ppt will give a brief idea upon this topic.

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  1. UNITS AND DIMENSIONS Chapter- 1
  2. What is P si ? ICS, the study of matter and energy, IS ananclent an broad field of Science. The word 'physics' comes from the Greek knowledge of nature,' and in general, the field aims to analyze and understand the natural phenomena of the universe. It's often considered to be the most fundamental science. It provides a basis for all other sciences - without physics, you couldn't have biology, chemistry, or anything else! Mathematics is the language of Physics. Without knowledge of Mathematics it would be much more difficult to discover, understand, and explain laws of nature. Units - All physical quantities are measured w.r.t. standard magnitude of the same physical quantity and these standards are called UNITS. eg. second, meter, kilogram, etc. So the four basic properties of units are: They must be well defined. 1. 2. They should be easily available and reproducible. 2. 3. They should be invariable e.g. step as a unit of length is not invariable. 3. 4. They should be accepted to all. 4. e.g. if some body has to study 4 hrs, the numeric part 4 says that it is 4 times of the unit of time. The second part says that the unit chosen for time is hour.
  3. SET OF DAM o UANTITIES set of physical quantities which are completely independent of each other . Physical quantities is called Set of Fundamental Quantities. Physical Quantity Mass Length Time Temperature Current Units(SI) kg(kilogram) m (meter) s (second) K (kelvin) A (ampere) Units (CGS) cm s cd (candela) Luminous intensity Amount of substance mol Notations Theta 1 orA cd mol
  4. Ph (Sl Unit) Length (m) Mass (kg) Time(s) Electric Current (A) The distance travelled by light in vacuum in 1/299,792,458 second is called 1 metre. The mass of a cylinder made of platinum- iridium alloy kept at International Bureau of Weights and Measures is defined as 1 kilogram. The second is the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium- 133 atom. If equal currents are maintained in the two parallel infinitely long wires of negligible cross-section, so that the force between them is 2 x 10-7 Newton per metre of the wires, the current in any of the wires is called 1 Ampere.
  5. Ph (Sl Unit) Thermodynamic Temperature (K) Luminous Intensity(cd) The fraction 273.161 of the thermodynamic temperature of triple point of water is called 1 Kelvin 1 candela is the luminous intensity of a black body of surface area 1/600,000 m2 1 placed at the temperature of freezing platinum and at a pressure of 101,325 N/m2 , in the direction perpendicular to its surface. Amount of substance (mole) The mole is the amount of a substance that contains as many elementary entities as there are number of atoms in 0.012 kg of carbon-12
  6. e are two supplementary units o 1. Plane angle (radian) angle = arc / radius Theta= I / r 2. Solid Angle (steradian) System of Units : The common system of units are : 1' 1 -FPS system : The units of length, mass and time are respectively foot, pound and second. 2.CGS system : The units of length, mass and time are respectively centimeter, gram and second. 3.MKS system : The units of length, mass and time are respectively metre, kilogram and second. 4. The International system of units (SI units).
  7. Derived ntities e Physical quantities that depend upon other physical quantity for its measurement are known as derived quantities. The measurement of derived quantities directly depends upon other quantities. So in order to measure the derive quantity, one must measure the quantities that it depends upon. Except 7 fundamental quantities, all other quantities are derived quantities. Some examples of derived quantities are: Derived Units Volume Force Pressure Energy, work Erg (CGS) Gram-calorie Power Watt I (or lit) 0.001 m31000 cm3 Newton (SI)NI kg • m/s2 Dyne (CGS) 1 g •cm/s2 Pascal (Sl)Pa1 N/m2 Joule (SI)J 1 N • m = 1 kg • m2/s2 1 dyne • cm = 1 g • cm2/s2 cal 4.184 J = 4.184 kg • m2/s2 WI J/s = 1 kg • m2/s2
  8. Dimensions nsions of a physical quantity are the powers tow -t e ndamental quantities must be raised to represent the given physical quantity. In mechanics all physical quantities can be expressed in terms of mass (M), length (L) and time (T). Example : Force = mass x acceleration = Or, [MILT- and — [F] - CMLT 2] So, the dimensions of force are 1 in mass, 1 i] Dimensionless quantity In the equation then the quantity is called dimensionless. Examples : Strain, specific gravity, angle. They are ratio of two similar quantities. A dimensionless quantity has same numeric value in all system of units
  9. Relationships of the SI derived units with special names and symbols and the SI —1) base units Sl BASE UNITS kilog ra m kg MASS meter LENGTH second s TIME mole mol AMOUNT OF SUBSTANCE ampere ELECTRIC CURRENT kelvin THERMODYNAMIC TEMPERATURE candela cd LUMINOUS INTENSITY Derived units without special names 3 VOLUME 2 AREA mps VELOCITY 2 ACCELERATION Sl DERIVED UNITS WITH SPECIAL NAMES AND SYMBOLS Solid lines indicate multiplication, broken lines indicate division (kg •m/s2) newton FORCE joule (N.rn) ENERGY, WORK QUANTITY OF HEAT katal (molls) CATALYTIC ACTIVITY Ecoulomb c ELECTRIC CHARGE deg ree Celsius oc CELSIUS TEMPERATURE UCC = -273.15 (Irn/m2) lux Ix ILLUMINANCE (N/m2) pascal Pa PRESSURE, STRESS watt POWER, HEAT FLOW RATE weber Wb MAGNETIC FLUX farad CAPACITANCE lumen (cd•sr) 1m LUMINOUS FLUX gray ABSORBED DOSE becquerel ACTIVITY COFA RADIONXL/OE) henry 'NOUCTANCE volt POTENTIAL, ELECTROMOTIVE FORCE ohm RESISTANCE (J/kg) oose EQUIVALENT FREQUENCY steradian MAGNETIC FLUX DENSITY siemens s CONDUCTANCE radian (m2fm2 = 1) sr SOLID ANGLE (rn/m rad PLANE ANGLE the diagram the derivation of each derived unit is indicated by arrows that bring in units in the numerator (solid lines) and units in the denominator (broken lines), as appropriate,
  10. Uses of Dimension Ional consistency of of any equa h srcäl sense must be identical. Otherwise, an equality in one system wou d be broken upon conversion to another system. This fact is used to obtain derived units from fundamental units. Example In the LMT class, the dimension of mass is M, the dimension of acceleration is LT—2, the Dimension of force can be obtained (derived) from Newton's second law: f = ma [f] = [m] [a] = MLT-2 In other words, in the LMT class, the dimension of force is LMT—2. We can determine the unknown exponent "?" in the following equation by requiring the same units on both sides: ML2T-2 = M(LT-I)? This is one technique of Dimensional Analysis, which can allow us to identify the controlling physical quantities in unfamiliar or complicated quantities.
  11. Limi NDimensionaI Ana Dimensional method can not be used to derive equation involving addition or subtraction. o In some cases, it is difficult to guess the factors while deriving the relation connecting two or more physical quantities. Equations using trigonometric, exponential or logarithmic expression can not be deduced. o If dimensions are given , physical quantity may not be unique as many physical quantities having same dimensions. For example dimensional formula of a physical quantity is ML2T-2, it may be work or energy or torque.
  12. Limi NDimensionaI Ana o It cannot be used if the physical quantity is dependent on more than three unknown variables. This method cannot be used in an equation containing two or more variables with same dimensions. Equation of frequency of a tuning fork f=(d/L2)v can not be derived by theory of dimension but can be checked.

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