Chapter 1
Units, Vectors
Theories and Experiments
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The goal of physics is to develop theories
based on experiments
A theory is a “guess,” expressed
mathematically, about how a system
works
The theory makes predictions about how a
system should work
Experiments check the theories’
predictions
Every theory is a work in progress
Units
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To communicate the result of a
measurement for a quantity, a unit
must be defined
Defining units allows everyone to
relate to the same fundamental
amount
Systems of Measurement
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Standardized systems
• agreed upon by some authority, usually
a governmental body
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SI -- Systéme International
• agreed to in 1960 by an international
committee
• main system used in this text
• also called mks for the first letters in the
units of the fundamental quantities
Time
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Units
• seconds, s
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Defined in terms of the oscillation of
radiation from a cesium atom
US “Official” Atomic Clock
Length
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Units
• SI – meter, m
• US Customary – foot, ft
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Defined in terms of a meter – the
distance traveled by light in a
vacuum during a given time
Mass
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Units
• SI – kilogram, kg
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Defined in terms of kilogram, based
on a specific cylinder kept at the
International Bureau of Weights and
Measures
Standard Kilogram
Multipliers
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Prefixes correspond to powers of 10
Each prefix has a specific name
Each prefix has a specific
abbreviation
Larger: kilo(k), Mega (M), etc
Small: milli (m), micro(), nano(n)
Trigonometry Review
Consider right triangle
opposite side
sin  
hypotenuse
adjacent side
cos  
hypotenuse
opposite side
tan  
adjacent side
More Trigonometry
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Pythagorean Theorem
o a h
2
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2
2
To find an angle, you need the
inverse trig function
• for example,
  sin1 0.707  45
Be sure your calculator is set
appropriately for degrees or radians
Vectors in Physics
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Quantities with both magnitude and
direction
• Displacement, velocity, acceleration,
force, etc.
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Scalars with only magnitude
• Mass, energy, time, temperature, etc.
Displacement Vector
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Specify both magnitude and direction
of physical displacement
• Length d
• Angle  (30° N of E)
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Vector in general
• Magnitude A
• Direction 
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Coordinates
Vector addition
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Graphical method
• Geometry
• Trigonometry
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Ex. Joe heads 4 blocks north & then
heads 4 blocks east
a) Graphical method
b) Geometrical method
Vector Addition
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Component Method
• Rectangular components
Ax  A cos( )
Ay  A sin(  )
• Add the corresponding components
• Back to magnitude angle form
A A  A
2
x
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Vector subtraction
2
y
  tan 1 ( Ay / Ax )
Example
Joe heads 100 m north & then heads
50 m 30° N of E.
a) Magnitude of the displacement
b) Direction
Example
Let vector A be 30 m, 30° N of E.
Let vector B be 30 m, 30° S of E.
Find A-B.
Scientific notation
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Expresses large & small numbers in
power of 10
Addition & subtraction
• Only with the same exponent
• Change to the same exponent
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Multiplication & division