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Ch-2

Units &Dimensions

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Lost in space

In September 1999, the UnitedStates lost theMars Climate Orbiteras it approached Mars. The loss ofthe $125 million spacecraft was dueto scientists confusing English units

and metric units.

Two spacecraft teams, one atNASAs Jet Propulsion Lab (JPL)

in Pasadena, CA, and the other at aLockheed Martin facility inColorado, where the spacecraft wasbuilt, were unknowingly exchangingsome vital information in differentunits.

The missing Mars Climate Orbiter

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Lost in space.

The spacecraft team inColoradoused English units ofpounds offorce to describe small forcesneeded to adjust the spacecrafts

orbit. The data was shipped via

computer, without units, to the JPL,where the navigation team wasexpecting the to receive the data inmetric measure.The mix-up in units led to the JPL

scientists giving the spacecraftscomputer wrong information, whichthrew the spacecraft off course.

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DIMENSION

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Dimension

Definition:

A physical property of every quantitywhich distinguishes it from all other

quantities is called dimension.

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Dimension

Length, mass, andtimeetc

are thefundamental dimensionson which the

measurement of all physical quantities is dependent

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UNITS

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UNITS A number alone is not sufficient to describe

a physical quantity. For example, to say that"a pipe must be 4 long " has no meaningunless a unit of measurement for length isalso specified. By adding units to thenumber, it becomes clear, "a pipe must be 4feet long ."

To specify and perform calculations withphysical quantities, the physical quantitiesmust be defined both in kind and magnitude.

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Units

Definition:

The standard measure of each kind ofphysical quantity is called aUNIT.

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Types of SI units

SI units are divided into Three:

Fundamental Units (or Base Units)

Derived Units

Supplementary Units

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Caution !!!

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Base Units details

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Base Units details

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Derived Units

Derived Units: Units formed by combining baseunits, supplementary units and other derived

units according to algebraic relations linking the

corresponding quantities.

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The Supplementary Units

In SI System two special units, called

supplementary units are used. These are

radian (plane angle)

steradian (solid angle)

Example radian: the plane angle given as the ratio of the

circular arc length subtended to the radius of the

circle.

a length divided by a length

sr=s/r

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The SI System

SI Prefixes 1 000 000 000 = 109 giga

1 000 000 = 106 mega

1 000 = 103 kilo

0.1 = 10-1 deci 0.01 = 10-2 centi

0.001 = 10-3 milli

0.000 001 = 10-6 micro

0.000 000 001 = 10-9 nano

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Dimensional Analysis

dimensional analysis is a tool to understandthe properties of physical quantities

independent of the units used to measure

them.

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Dimensional Analysis.

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