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Copyright © 2012 Pearson Education Inc.
PowerPoint® Lectures for University Physics, Thirteenth Edition – Hugh D. Young and Roger A. Freedman
Lectures by Wayne Anderson
Chapter 1
Units, Physical Quantities, and Vectors
Copyright © 2012 Pearson Education Inc.
Goals for Chapter 1 • To learn three fundamental quantities of physics and the
units to measure them
• To keep track of significant figures in calculations
• To understand vectors and scalars and how to add vectors graphically
• To determine vector components and how to use them in calculations
• To understand unit vectors and how to use them with components to describe vectors
• To learn two ways of multiplying vectors
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The nature of physics
• Physics is an experimental science in which physicists seek patterns that relate the phenomena of nature.
• The patterns are called physical theories.
• A very well established or widely used theory is called a physical law or principle.
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Solving problems in physics • A problem-solving strategy offers techniques for setting up
and solving problems efficiently and accurately.
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Why use units
• This table is 1000 long.
• This table is 1 long.
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Why have different units
• The speed of a car is 26 m/s.
• The speed of a car is 26,000 mm/s.
• A pencil is 15 cm long.
• A pencil is 0.00015 km long.
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Standards and units
• Length, time, and mass are three fundamental quantities of physics.
• The International System (SI for Système International) is the most widely used system of units.
• In SI units, length is measured in meters, time in seconds, and mass in kilograms.
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What is one meter
• The meter is the basic unit of length in the SI system of units. The meter is defined to be the distance light travels through a vacuum in exactly 1/299792458 seconds.
• U.S. PROTOTYPE METER BAR
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What is one kilogram
• It is defined as the mass of a particular international prototype made of platinum-iridium and kept at the International Bureau of Weights and Measures. It was originally defined as the mass of one liter (10-3 cubic meter) of pure water.
• France holds the world's standard for the kilogram weight. It's a cylinder-shaped object that has dictated all other kilogram weights for 130 years now.
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What is one second
• The second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom.
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Unit prefixes
• Table 1.1 shows some larger and smaller units for the fundamental quantities.
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More prefix for powers of ten yotta- (Y-) 1024 1 septillion zetta- (Z-) 1021 1 sextillion exa- (E-) 1018 1 quintillion peta- (P-) 1015 1 quadrillion tera- (T-) 1012 1 trillion giga- (G-) 109 1 billion mega- (M-) 106 1 million kilo- (k-) 103 1 thousand hecto- (h-) 102 1 hundred deka- (da-) 10 1 ten deci- (d-) 10-1 1 tenth centi- (c-) 10-2 1 hundredth milli- (m-) 10-3 1 thousandth micro- (µ-) 10-6 1 millionth nano- (n-) 10-9 1 billionth pico- (p-) 10-12 1 trillionth femto- (f-) 10-15 1 quadrillionth atto- (a-) 10-18 1 quintillionth zepto- (z-) 10-21 1 sextillionth yocto- (y-) 10-24 1 septillionth
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British System vs. SI Length kilometer (km) = 1,000 m 1 km = 0.621 mi 1 mi = 1.609 km meter (m) = 100 cm 1 m = 3.281 ft 1 ft = 0.305 m centimeter (cm) = 0.01 m 1 cm = 0.394 in. 1 in. = 2.540 cm millimeter (mm) = 0.001 m 1 mm = 0.039 in. micrometer (µm) = 0.000 001 m nanometer (nm) = 0.000 000 001 m Area square kilometer (km2) = 100 hectares 1 km2 = 0.386 mi2 1 mi2 = 2.590 km2 hectare (ha) = 10,000 m2 1 ha = 2.471 acres 1 acre = 0.405 ha square meter (m2) = 10,000 cm2 1 m2 = 10.765 ft2 1 ft2 = 0.093 m2 square centimeter (cm2) = 100 mm2 1 cm2 = 0.155 in.2 1 in.2 = 6.452 cm2 Volume liter (L) = 1,000 mL = 1 dm3 1 L = 1.057 fl qt 1 fl qt = 0.946 L milliliter (mL) = 0.001 L = 1 cm3 1 mL = 0.034 fl oz 1 fl oz = 29.575 mL microliter (µL) = 0.000 001 L Mass kilogram (kg) = 1,000 g 1 kg = 2.205 lb 1 lb = 0.454 kg gram (g) = 1,000 mg 1 g = 0.035 oz 1 oz = 28.349 g milligram (mg) = 0.001 g
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Unit consistency and conversions • An equation must be dimensionally consistent. Terms to be added
or equated must always have the same units. (Be sure you’re adding “apples to apples.”)
• Always carry units through calculations. • Convert to standard units as necessary. (Follow Problem-Solving
Strategy 1.2) • Follow Examples 1.1 and 1.2.
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Uncertainty and significant figures—Figure 1.7 • The uncertainty of a measured quantity
is indicated by its number of significant figures.
• For multiplication and division, the answer can have no more significant figures than the smallest number of significant figures in the factors.
• For addition and subtraction, the number of significant figures is determined by the term having the fewest digits to the right of the decimal point.
• Refer to Table 1.2, Figure 1.8, and Example 1.3.
• As this train mishap illustrates, even a small percent error can have spectacular results!
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Ways to express accuracy
• 56.47 ± 0.02
• 47 ± 10% (fractional/percent error, fractional/percent uncertainty)
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Estimates and orders of magnitude
• An order-of-magnitude estimate of a quantity gives a rough idea of its magnitude.
• Can you count 1 million in your life?
• Follow Example 1.4.
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Vectors and scalars
• A scalar quantity can be described by a single number.
• A vector quantity has both a magnitude and a direction in space.
• In this book, a vector quantity is represented in boldface italic type with an arrow over it: A.
• The magnitude of A is written as A or |A|.
è
è è
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Drawing vectors—Figure 1.10 • Draw a vector as a line with an arrowhead at its tip.
• The length of the line shows the vector’s magnitude.
• The direction of the line shows the vector’s direction.
• Figure 1.10 shows equal-magnitude vectors having the same direction and opposite directions.
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Adding two vectors graphically—Figures 1.11–1.12 • Two vectors may be added graphically using either the parallelogram
method or the head-to-tail method.
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Adding more than two vectors graphically—Figure 1.13
• To add several vectors, use the head-to-tail method.
• The vectors can be added in any order.
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Subtracting vectors
• Figure 1.14 shows how to subtract vectors.
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Multiplying a vector by a scalar
• If c is a scalar, the product cA has magnitude |c|A.
• Figure 1.15 illustrates multiplication of a vector by a positive scalar and a negative scalar.
è
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Addition of two vectors at right angles • First add the vectors graphically.
• Then use trigonometry to find the magnitude and direction of the sum.
• Follow Example 1.5.
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Components of a vector—Figure 1.17 • Adding vectors graphically provides limited accuracy. Vector
components provide a general method for adding vectors.
• Any vector can be represented by an x-component Ax and a y-component Ay.
• Use trigonometry to find the components of a vector: Ax = Acos θ and Ay = Asin θ, where θ is measured from the +x-axis toward the +y-axis.
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Positive and negative components—Figure 1.18
• The components of a vector can be positive or negative numbers, as shown in the figure.
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Finding components—Figure 1.19 • We can calculate the components of a vector from its magnitude
and direction.
• Follow Example 1.6.
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Calculations using components • We can use the components of a vector to find its magnitude
and direction:
• We can use the components of a set of vectors to find the components of their sum:
• Refer to Problem-Solving Strategy 1.3.
2 2 and tanθ= + = yx y
x
AA A A A
, = + + + = + + +L Lx x x x y y y yR A B C R A B C
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Adding vectors using their components—Figure 1.22
• Follow Examples 1.7 and 1.8.
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Unit vectors—Figures 1.23–1.24
• A unit vector has a magnitude of 1 with no units.
• The unit vector î points in the +x-direction, ĵ points in the +y-direction, and points in the +z-direction.
• Any vector can be expressed in terms of its components as A =Axî+ Ay + Az .
• Follow Example 1.9. j$j$
k$k$
k$k$
è
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The scalar product—Figures 1.25–1.26
• The scalar product (also called the “dot product”) of two vectors is
• Figures 1.25 and 1.26 illustrate the scalar product.
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Calculating a scalar product
[Insert figure 1.27 here]
• In terms of components, • Example 1.10 shows how to calculate a scalar product in two
ways.
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Finding an angle using the scalar product
• Example 1.11 shows how to use components to find the angle between two vectors.
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The vector product—Figures 1.29–1.30 • The vector
product (“cross product”) of two vectors has magnitude
and the right-hand rule gives its direction. See Figures 1.29 and 1.30.
|rA×rB | = ABsinφ
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Calculating the vector product—Figure 1.32
• Use ABsinΦ to find the magnitude and the right-hand rule to find the direction.
• Refer to Example 1.12.
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