SI Units

SI Units

Physics 131 - Physics for Health, Life and Environmental Sciences

• Meter – The distance travelled by light in a vacuum during a time period of s

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Diameter of a nucleus: 1x 10-14 mDiameter of an atom: 1x 10-10 mLength of an average cell: 1x 10-5 mLength of a car: 4 mFootball Field: 9x 101 mAvg. distance of the earth to the moon: 3.84x 108 m

Abdul Mirza CENTRE FOR QUANTUM TECHNOLOGY, SCHOOL OF PHYSICS, UKZN

SI Units



• Kilogram – The exact weight of a specific cylinder of a platinum-iridium alloy housed at the International Bureau of Weights and Measures, France

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Electron: 9.1x 10-31 kgMosquitoe: 1x 10-5 kgHuman: 1x 102 kgElephant: 5x 103 kgEarth: 5.98x 1024 kg

SI Units



• Second – 9 192 631 770 times the period of the radiation emitted from a caesium atom

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Duration of a nuclear collision: 1x 10-22 sReaction time of humans: 2x 10-1 sTime difference between 1st and 2nd position at indycar race: 1.4 s (difference in price money: $650 000)1 year: 3.2x 107 sCalculated age of the universe: 5x 1017 s

Unit Conversions



• How do we shift a quantity between units?

• Multiply through by the conversion ratio

Convert 10 000s to hours.

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s

hs3600

110000 hh 778.2

3600

10000

Types of Quantities



• A quantity is measurable property of an object.• A Car:

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No. of seatsDistance travelled

Speed

Height

Length

Temperature

All these quantities just have a magnitude - Scalars

Types of Quantities



• Lets look at the car again:

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Speed in a particular direction

‘Distance’ covered from a certain point Air friction

against motion of car

Velocity

Drag Force

Displacement

The above quantities, together with a magnitude, act or have acted in a specific direction.

Scalars vs. Vectors



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Scalars:

• Has magnitude only

• Distance: The physical length of a path between two points.• Speed: The rate of change distance.

• Mass: The quantity of matter of a particular object.

Vectors:

• Has magnitude and direction

• Displacement: The line-of-sight distance from one point to another. • Velocity: The rate of change of displacement in a particular direction.• Weight: The gravitational force exerted on an object by the earth.

Vectors



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• Vectors have magnitude and direction.• In Cartesian co-ordinates, one can represent them as arrows.• The length of the arrow is the magnitude.• The direction of the arrow is the direction of the vector.

y-axis

z-axis

x-axis

Each axis has a basic vector from which all others can be constructed: Basis Vectors

x axis, i vector: (1,0,0)

z axis, k vector: (0,0,1)

y axis, j vector: (0,1,0)

|i| = |j| = |k| = 1

Vectors



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Vectors by convention always start at the origin

The yellow vector, r, can be written as the sum of all the smaller base vectors:

r = 2i + 3j + 6k = (2,3,6)

We can split the motion up into three components:• X component - x = 2i• Y component - y = 3j• Z component - z = 6k

Vectors



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To calculate the magnitude of a vector, one uses Pythagoras:

Construct the vector, R = (x,y):

R = (3,9)R = (-2,4)R = 6i -1j

What is the magnitude and direction of each vector?

x

Ry 222 yxR

Components of Vectors



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To calculate the components of a vector, one uses trig rules:

x = Rcosθ

y = Rsinθ

x

Ry

θ

Mathematics of Vectors



• Vectors can be added/subtracted to/from each other, however the direction is important.

• A vector can be multiplied by a scalar. The result is a vector of different magnitude but its direction remains unchanged.

• Vectors can be multiplied together, but the directions must be taken into account.– Weird things happen

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SI Units

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