SI Units
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This document discusses SI units and vectors. It defines the meter based on the speed of light, kilogram based on a platinum-iridium cylinder, and second based on a caesium atom's radiation. It provides examples of lengths, masses and times ranging from the diameter of a nucleus to the age of the universe. Vectors are defined as having both magnitude and direction, unlike scalars. Components of vectors and their addition/subtraction are also covered.
SI Units
- 1. SI Units Meter – The distance travelled by light in a vacuum during a time period of s Physics 131 - Physics for Health, Life and Environmental Sciences Diameter of a nucleus: 1x 10 -14 m Diameter of an atom: 1x 10 -10 m Length of an average cell: 1x 10 -5 m Length of a car: 4 m Football Field: 9x 10 1 m Avg. distance of the earth to the moon: 3.84x 10 8 m Abdul Mirza CENTRE FOR QUANTUM TECHNOLOGY, SCHOOL OF PHYSICS, UKZN
- 2. 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 Physics 131 - Physics for Health, Life and Environmental Sciences Electron: 9.1x 10 -31 kg Mosquitoe: 1x 10 -5 kg Human: 1x 10 2 kg Elephant: 5x 10 3 kg Earth: 5.98x 10 24 kg Abdul Mirza CENTRE FOR QUANTUM TECHNOLOGY, SCHOOL OF PHYSICS, UKZN
- 3. SI Units Second – 9 192 631 770 times the period of the radiation emitted from a caesium atom Physics 131 - Physics for Health, Life and Environmental Sciences Duration of a nuclear collision: 1x 10 -22 s Reaction time of humans: 2x 10 -1 s Time difference between 1 st and 2 nd position at indycar race: 1.4 s (difference in price money: $650 000) 1 year: 3.2x 10 7 s Calculated age of the universe: 5x 10 17 s Abdul Mirza CENTRE FOR QUANTUM TECHNOLOGY, SCHOOL OF PHYSICS, UKZN
- 4. Unit Conversions How do we shift a quantity between units? Multiply through by the conversion ratio Convert 10 000s to hours. Physics 131 - Physics for Health, Life and Environmental Sciences Abdul Mirza CENTRE FOR QUANTUM TECHNOLOGY, SCHOOL OF PHYSICS, UKZN
- 5. Types of Quantities A quantity is measurable property of an object. A Car: Physics 131 - Physics for Health, Life and Environmental Sciences No. of seats Distance travelled Speed Height Length Temperature All these quantities just have a magnitude - Scalars Abdul Mirza CENTRE FOR QUANTUM TECHNOLOGY, SCHOOL OF PHYSICS, UKZN
- 6. Types of Quantities Lets look at the car again: Physics 131 - Physics for Health, Life and Environmental Sciences 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. Abdul Mirza CENTRE FOR QUANTUM TECHNOLOGY, SCHOOL OF PHYSICS, UKZN
- 7. Scalars vs. Vectors Physics 131 - Physics for Health, Life and Environmental Sciences 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. Abdul Mirza CENTRE FOR QUANTUM TECHNOLOGY, SCHOOL OF PHYSICS, UKZN
- 8. Vectors Physics 131 - Physics for Health, Life and Environmental Sciences 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 Abdul Mirza CENTRE FOR QUANTUM TECHNOLOGY, SCHOOL OF PHYSICS, UKZN
- 9. Vectors Physics 131 - Physics for Health, Life and Environmental Sciences 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 = 2 i + 3 j + 6 k = (2,3,6) We can split the motion up into three components: X component - x = 2 i Y component - y = 3 j Z component - z = 6 k Abdul Mirza CENTRE FOR QUANTUM TECHNOLOGY, SCHOOL OF PHYSICS, UKZN
- 10. Vectors Physics 131 - Physics for Health, Life and Environmental Sciences To calculate the magnitude of a vector, one uses Pythagoras: Construct the vector, R = (x,y): R = (3,9) R = (-2,4) R = 6 i -1 j What is the magnitude and direction of each vector? x R y Abdul Mirza CENTRE FOR QUANTUM TECHNOLOGY, SCHOOL OF PHYSICS, UKZN
- 11. Components of Vectors Physics 131 - Physics for Health, Life and Environmental Sciences To calculate the components of a vector, one uses trig rules: x = R cos θ y = R sin θ x R y θ Abdul Mirza CENTRE FOR QUANTUM TECHNOLOGY, SCHOOL OF PHYSICS, UKZN
- 12. 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 Physics 131 - Physics for Health, Life and Environmental Sciences Abdul Mirza CENTRE FOR QUANTUM TECHNOLOGY, SCHOOL OF PHYSICS, UKZN