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Chapter 1 Introduction, Units, and Dimensional Analysis

Chapter 1 Introduction, Units, and Dimensional Analysis. Learning Objectives Physics and the Laws of Nature Units of Length, Mass, and Time Dimensional Analysis Converting Units Order-of-Magnitude Calculations Scalars and Vectors Problem Solving in Physics.

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Chapter 1 Introduction, Units, and Dimensional Analysis

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  1. Chapter 1 Introduction, Units, and Dimensional Analysis • Learning Objectives • Physics and the Laws of Nature • Units of Length, Mass, and Time • Dimensional Analysis • Converting Units • Order-of-Magnitude Calculations • Scalars and Vectors • Problem Solving in Physics PowerPoint presentations are compiled from Walker 3rd Edition Instructor CD-ROM and Dr. Daniel Bullock’s own resources

  2. Why do we study physics? • Physics is the study of the fundamental laws of nature. • Aristotle  16th century • Galileo  Law of Inertia • Newton  17th century • Principia • Three laws of motion • Modern Physics  19th century

  3. Mathematical Nature of Physics • Newton and Leibniz  Calculus • Mathematics is the only language precise enough to accurately describe the laws of nature.  isomorphism • Skills needed for success in this course • Algebra • Trigonometry • Vector Algebra • Graphical Analysis

  4. Units used in Physics • Fundamental units • Length (International System, SI meter (m), British  foot (ft)) • Mass (SI gram (gr), British  slug (sl)) • Time (SI & British  second (s)) • Derived units – combinations of fundamental units • Speed (SI  m/s, British  ft/s) • Acceleration (SI  m/s2, British  ft/s2) • Force = mass × acceleration (SI  kg·m/s2 = Newton (N), British  pounds (lbs)

  5. Units used in Physics • Length: the meter • Was: one ten-millionth of the distance from the North Pole to the equator • Now: the distance traveled by light in a vacuum in 1/299,792,458 of a second

  6. Units used in Physics • Mass: the kilogram • One kilogram is the mass of a particular platinum-iridium cylinder kept at the International Bureau of Weights and Standards, Sèvres, France.

  7. Units used in Physics • Time: the second • One second is the time for radiation from a cesium-133 atom to complete 9,192,631,770 oscillation cycles.

  8. Converting units in the SI system • SI system based on powers of ten • Each prefix represents a different power of ten Kind Hector Decked Mr. Deci at the Cinema on Monday

  9. Dimensional Analysis • Any valid physical formula must be dimensionally consistent – each term must have the same dimensions From the table: Distance = velocity × time Velocity = acceleration × time Energy = mass × (velocity)2

  10. Converting Units • Converting feet to meters: 1 m = 3.281 ft (this is a conversion factor) Or: 1 = 1 m / 3.281 ft 316 ft × (1 m / 3.281 ft) = 96.3 m Note that the units cancel properly – this is the key to using the conversion factor correctly! • Converting feet2 = meter2 316 ft2 × (1 m / 3.281 ft)2 = 29.35 m2

  11. Scalars and Vectors • Scalar – a numerical value. May be positive or negative. Examples: temperature, speed, height • Vector – a quantity with both magnitude and direction. Examples: displacement (e.g., 10 feet north), force, magnetic field

  12. Problem Solving in Physics • Read the problem carefully • Sketch the system • Visualize the physical process • Strategize • Identify appropriate equations • Solve the equations • Check your answer • Explore limits and special cases

  13. Chapter 1 Summary • Physics is based on a small number of laws and principles • Units of length are meters; of mass, kilograms; and of time, seconds • All terms in an equation must have the same dimensions • Convert one unit to another by multiplying by their ratio • Scalars are numbers; vectors have both magnitude and direction • Problem solving: read, sketch, visualize, strategize, identify equations, solve, check, explore limits

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