The purpose of the session

• Discuss basic and derived units and measurements

• Estimate the physical quantities• Explain Newton’s laws of motion• Explain Scalar and Vector

The International System of Units (SI)

The International System of Units (SI) defines seven unitsof measure as a basic set from which all other SI unitsare derived. The SI base units and their physicalquantities are:• metre (m) for length• kilogram(kg) for mass• second(s) for time• ampere (A)for electric current• Kelvin(K) for temperature• Candela(cd) for luminous intensity• Mole(mol) for the amount of substance

Symbols are written in lowercase except when named after person.

Unit of length m

The metre is the length of the path travelled bylight in vacuum during a time interval of 1/299792 458 of a second.1 ⁄ 10,000,000 of the distance from the Earth'sequator to the North Pole measured on thecircumference through Paris

Dimension symbol; L

Instruments

Unit of mass kg

The kilogram is the unit of mass; it is equal tothe mass of the international prototype of thekilogram.The mass of one litre of water. A litre is onethousandth of a cubic metre.

Dimension symbol; M

Unit of Time s

The second is the duration of 9 192 631 770 periodsof the radiation corresponding to the transitionbetween the two hyperfine levels of the groundstate of the cesium 133 atom.The day is divided in 24 hours, each hour divided in60 minutes, each minute divided in 60 seconds.A second is 1 ⁄ (24 × 60 × 60) of the day.

Dimension symbol T

Unit of electric current AThe ampere is that constant current which, if maintainedin two straight parallel conductors of infinite length, ofnegligible circular cross-section, and placed 1 meter apartin vacuum, would produce between these conductors aforce equal to 2 x 10-7 newton per meter of length.

The original "International Ampere" was definedelectrochemically as the current required to deposit 1.118milligrams of silver per second from a solution of silver nitrate.Compared to the SI ampere, the difference is 0.015%.

Dimension symbol; l

Electric Current A

Unit of thermodynamic temperatureK

The Kelvin, unit of thermodynamic temperature,is the fraction 1/273.16 of the thermodynamictemperature of the triple point of water.

The Celsius scale: the Kelvin scale uses thedegree Celsius for its unit increment, but is athermodynamic scale (0 K is absolute zero).

Dimension symbol; θ

Unit of amount of substancemol

The mole is the amount of substance of a systemwhich contains as many elementary entities asthere are atoms in 0.012 kilogram of carbon 12; itssymbol is "mol.“

When the mole is used, the elementary entities must bespecified and may be atoms, molecules, ions, electrons,other particles, or specified groups of such particles.

Atomic weight or molecular weight divided by the molar massconstant, 1 g/mol.

Dimension symbol; n

Unit of luminous intensitycd

The candela is the luminous intensity, in a givendirection, of a source that emits monochromaticradiation of frequency 540 x 1012 hertz and thathas a radiant intensity in that direction of 1/683watt per steradian.

The candlepower, which is based on the lightemitted from a burning candle of standardproperties.

Dimension symbol; J

Derived Units

The International System of Units (SI) specifies aset of seven base units from which all otherSI units of measurement are derived. Each ofthese other units (SI derived units) iseither dimensionless or can be expressed as aproduct of (positive or negative, but usuallyintegral) powers of one or more of the baseunits.

Derived UnitsName Symbol Quantity SI equivalencyHertz Hz frequency s−1

Radian rad, angle dimensionlessNewton N force, weight kg m s⋅ ⋅ −2

Pascal Pa pressure, stress kg m⋅ −1 s⋅ −2

Joule J energy, work, heat kg m⋅ 2 s⋅ −2

watt W power, radiant flux kg m⋅ 2 s⋅ −3

coulomb C electric charge s A ⋅ volt V voltage, electrical potential difference, electromotive force kg m⋅ 2 s⋅ −3 A⋅ −1 farad F electrical capacitance kg−1 m⋅ −2 s⋅ 4 A⋅ 2 ohm Ω electrical resistance, impedance, reactance kg m⋅ 2 s⋅ −3 A⋅ −2

SI prefixes

A SI prefix is a name that is added to the name of a basicunit and which indicates whether that unit is a multiple(or a fraction) of that unit.

For example, the prefix "kilo“added to "meter" gives "kilometer", which is a unit 1 000times LARGER than the base unit "meter". Similarly, theprefix "milli" added to "gram" gives "milligram", which isa unit 1 000 times SMALLER than the base unit "gram".

The table shown next slide lists the names of approved SIprefixes.

SI prefixes

Physical Quantity

A physical quantity (or "physical magnitude") is a physical property of a phenomenon, body, orsubstance, that can be quantified by measurement.A physical quantity can be expressed as thecombination of a number – usually a real number –and a unit or combination of units; forexample, 1.6749275×10−27 kg (the mass ofthe neutron), or299792458 metres persecond (the speed of light).

Newton's laws of motion

Newton's laws of motion are three physicallaws that, together, laid the foundationfor classical mechanics. They describe therelationship between a body andthe forces acting upon it, and its motion inresponse to those forces. They have been expressedin several different ways, over nearly threecenturies, and can be summarised as follows.

First law:When viewed in an inertial reference frame, anobject either remains at rest or continues tomove at a constant velocity, unless acted uponby a force.The first law can be stated mathematically as

Consequently,An object that is at rest will stay at rest unless aforce acts upon it.An object that is in motion will not change itsvelocity unless a force acts upon it.

Second law:

The vector sum of the forces F on an object isequal to the mass m of that object multiplied bythe acceleration vector a of the object: F = ma.The net force on an object is equal to the rate ofchange (that is, the derivative) of its linearmomentum p in an inertial reference frame:

Third law:When one body exerts a force on a second body, the second bodysimultaneously exerts a force equal in magnitude and opposite indirection on the first body.

The third law states that all forces between two objects exist in equalmagnitude and opposite direction: if one object A exerts a force FA on asecond object B, then B simultaneously exerts a force FB on A, and the twoforces are equal and opposite: FA = −FB. The third law means that all forcesare interactions between different bodies, and thus that there is no suchThing as a unidirectional force or a force that acts on only one body.

Scalar and Vector

Properties of vectors

• Two vectors are equal if they have the same magnitude and the same direction.

• Just like scalars which can have positive or negative values, vectors can also be positive or negative. A negative vector is a vector which points in the direction opposite to the reference positive direction. For example, if in a particular situation, we define the upward direction as the reference positive direction, then a force F1−→=30 N downwards would be a negative vector and could also be written as F1−→=−30 N. In this case, the negative (-) sign indicates that the direction of F1−→ is opposite to that of the reference positive direction.

• A negative vector is a vector that has the opposite direction to the reference positive direction.

Addition and Subtraction of Vectors

Resultant of Forces

Multiplication of vector

Multiplication of Vector

Dot Product

Cross Product