Physics 1321 Chapter 1 Lecture Slides.pdf

Lectures by Jason Harlow
PowerPoint® Lectures for
University Physics, 14th Edition
– Hugh D. Young and Roger A. Freedman
Units, Physical Quantities, and
Vectors
Chapter 1
© 2016 Pearson Education Inc.

Learning Goals for Chapter 1
Looking forward at …
• the four steps you can use to solve any physics problem.
• three fundamental quantities of physics and the units
physicists use to measure them.
• how to work with units and significant figures in your
calculations.
• how to add and subtract vectors graphically, and using vector
components.
• two ways to multiply vectors: the scalar (dot) product and the
vector (cross) product.

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.

Solving problems in physics
• All of the Problem-Solving Strategies and Examples in this
book will follow these four steps:
• Identify the relevant concepts, target variables, and known
quantities, as stated or implied in the problem.
• Set Up the problem: Choose the equations that you’ll use to
solve the problem, and draw a sketch of the situation.
• Execute the solution: This is where you “do the math.”
• Evaluate your answer: Compare your answer with your
estimates, and reconsider things if there’s a discrepancy.

Idealized models
To simplify the analysis of
(a) a baseball in flight, we use
(b) an idealized model.

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.

Unit prefixes
• Prefixes can be used to create larger and smaller units for the
fundamental quantities. Some examples are:
• 1 µm = 10−6 m (size of some bacteria and living cells)
• 1 km = 103 m (a 10-minute walk)
• 1 mg = 10−6 kg (mass of a grain of salt)
• 1 g = 10−3 kg (mass of a paper clip)
• 1 ns = 10−9 s (time for light to travel 0.3 m)

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, by forming a ratio of
the same physical quantity in two different units, and using it
as a multiplier.
• For example, to find the number of seconds in 3 min, we
write:

Uncertainty and significant figures
• 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.
• As this train mishap illustrates,
even a small percent error can have
spectacular results!

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: .
• The magnitude of is written as A or | |.

Drawing vectors
• 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.

Adding two vectors graphically

Adding more than two vectors graphically
• To add several vectors, use the head-to-tail method.
• The vectors can be added in any order.

Subtracting vectors

Multiplying a vector by a scalar
• If c is a scalar, the product
c has magnitude |c|A.
• The figure illustrates
multiplication of a vector
by (a) a positive scalar
and (b) a negative scalar.

Addition of two vectors at right angles
• To add two vectors that are at right angles, first add the
vectors graphically.
• Then use trigonometry to find the magnitude and direction of
the sum.
• In the figure, a cross-
country skier ends up
2.24 km from her
starting point, in a
direction of 63.4° east
of north.

Components of a vector
• 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.

Positive and negative components
• The components of a vector may be positive or negative
numbers, as shown in the figures.

Finding components
• We can calculate the components of a vector from its
magnitude and direction.

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.

Unit vectors
• A unit vector has a magnitude
of 1 with no units.
• The unit vector points in the
+x-direction, points in the
+y-direction, and points in
the +z-direction.
• Any vector can be expressed
in terms of its components as

The scalar product

The scalar product
The scalar product can be
positive, negative, or zero,
depending on the angle
between and .

Calculating a scalar product using
components
• In terms of components:
• The scalar product of two vectors is the sum of the products
of their respective components.

Finding an angle using the scalar product
• Example 1.10 shows how to use components to find the angle
between two vectors.

The vector product
If the vector product (“cross product”) of two vectors is
then:
The direction of the
vector product can be
found using the right-
hand rule:

The vector product is anticommutative

Calculating the vector product
• Use ABsinϕ to find the magnitude and the right-hand rule to
find the direction.
• Refer to Example 1.11.

Physics 1321 Chapter 1 Lecture Slides.pdf

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