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?
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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
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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 platinumiridium 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
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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