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

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

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

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)

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

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.

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.

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

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

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

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

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

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