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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 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
1.
2.
3.
4.
5.
6.
7.
8.
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