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CHAPTER 1 UNIT AND DIMENSION

CHAPTER 1 UNIT AND DIMENSION. OBJECTIVES. Ability to define and understand base and derived quantities, distinguish standard units and s y stem of unit, and fundamental quantities. Ability to understand and apply converting units within a system or from one system of unit to another

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CHAPTER 1 UNIT AND DIMENSION

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  1. CHAPTER 1 UNIT AND DIMENSION

  2. OBJECTIVES • Ability to define and understand base and derived quantities, distinguish standard units and system of unit, and fundamental quantities. • Ability to understand and apply converting units within a system or from one system of unit to another • Ability to understand and apply Dimensional Analysis.

  3. DEFINITION a physical quantity that can be counted or measured using standard size defined by custom or law. UNIT • Every measurement or quantitative statement requires a unit.  • Example: • If you say you’re driving a car 30 that doesn't mean anything. Are you driving it 30 miles/hour, 30 km/hour, or 30 ft/sec?  30 only means something when unit is attached to it. 

  4. STANDARD UNITS • If a unit becomes officially accepted, it’s called Standard Unit. • Group of Unit and Combination is called SYSTEM OF UNITS. Example: SI Units, British Units SI = International Systems of Units

  5. SI (Système International) Units also called Metric System • All things in classical mechanics can be expressed in terms of base quantities: • Length (L) , MASS (M), TIME (T) • British Units: • L = inches, feet, miles, • M =slugs (pounds), • T = seconds

  6. PHYSICAL QUANTITIES • Physics is based on physical quantities. Eg: length, mass, time, force and pressure. • Generally, physical quantity is a quantity that can be measured.

  7. BASE QUANTITIES IN SI SYSTEM

  8. DERIVED QUANTITIES FROM BASE QUANTITIES

  9. DIMENSION • From Latin word = "measured out" a parameter or measurement required to define the characteristics of an object - i.e.length, width, and height or size and shape.

  10. What are their units, dimensions and values? - 110mg of sodium - 24 hands high -5 gal of gasoline

  11. DIMENSIONAL ANALYSIS • PURPOSES: 1) TO CHECK THE EQUATION 2) ANALYSIS DIMENSION TO BUILD FORMULA • Example (to check equation): Distance, d=vt2 ( velocity x time2 ) • Dimension on left side [d] = L • Dimension on right side [vt2] = L / T x T2 = L x T • L=LT? Left units and right units don’t match, theequation must be wrong !!

  12. F = mvR (a) (b) (c) Remember: Force has dimensions of ML/T2 Example 1 • The force (F) to keep an object moving in a circle can be described in terms of the velocity, v, (dimension L/T) of the object, its mass, m, (dimension M), and the radius of the circle, R, (dimension L). • Which of the following formulas for Fcould be correct ?

  13. F = mvR (a) (b) (c) Solution Consider for RHS, since [F] = MLT-2 For (a); [mvR] = MLT-1L=ML2T-1 (incorrect) For (b); [mv2R-2] = ML2T-2L-2 = MT-2 (incorrect) For (c); [mv2R-1] = ML2T-2L-1 = MLT-2 (correct) Answer is (c)

  14. UNIT CONVERSIONS • To change units in different systems, or different units in the same system. • Example:

  15. Example 2 • A hall bulletin board has an area of 2.5 m2. What is area in cm2? Solution: conversion of area units (in the same SI unit: mks cgs). 1m = 100cm.So,

  16. Example 3 • Convert miles per hour to meters per second. Given: • 1 inch = 2.54 cm • 1 m = 3.28 ft • 1 mile = 5280 ft • 1 mile= 1.61 km Solution:

  17. QUIZ 1 • When on travel in Kedah you rent a small car which consumes 6 liters of gasoline per 100 km. What is the MPG (mile per gallons) of the car ? 1L=1000cm3=0.3531ft3, 1ft3=0.02832m3=7.481 gal

  18. SIGNIFICANT FIGURES • The number of digits that matter in a measurement or calculation. 1.all non-zero digits are significant. 2. in scientific notation all digits are significant 3. Zeros may or may not be significant. • those used to position the decimal point are not significant. • those used to position powers of ten ordinals may or may not be significant. • Examples: • 2 1 sig fig • 40 ambiguous, could be 1 or 2 sig figs • 4.0 x 1012 sig figs (scientific notation) • 0.0031 2 sig figs • 3.03 3 sig figs

  19. When multiplying or dividing, the answer should have the same number of significant figures as the least accurate of the quantities in the calculation. • When adding or subtracting, the number of digits to the right of the decimal point should equal that of the term in the sum or difference that has the smallest number of digits to the right of the decimal point. • Examples: • 2 x 3.1 = 6 • 3.1 + 0.004 = 3.1 • 4.0 x 101 2.04 x 102 =1.6 X 10-1

  20. END OF CHAPTER 1

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