# Overview of Course

Mechanics

Oct 24, 2013 (4 years and 6 months ago)

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Lecture 0: Introduction and
Overview of Course

Serway

and
Vuille

Ch. 1

Outline

What is physics?

Outline of course

SI units and conversion of units

Dimensional analysis

Uncertainty and significant figures

Introduction to Physics

The

goal

of

physics

is

to

provide

an

understanding

of

the

physical

world

by

developing

theories

based

on

experiments
.

A

physical

theory

describes

how

a

given

physical

system

works,

makes

prediction

the

physical

system,

and

can

be

falsified

by

observations

and

experiments
.

Introduction to Physics

The

common

subfields

of

physics

are

Classical

Mechanics

Thermodynamics

Electromagnetism

Quantum

Mechanics

Atomic

and

Nuclear

Physics

Relativity

Course Outline

Motion and Kinematics

Newton’s Laws of Motion and Dynamics

Energy and Energy Conservation

Momentum and Collisions

Newtonian Gravitation

Rotational Dynamics

Fluid Mechanics and Fluid Dynamics

Vibrations, Waves, and Sound

Thermal Physics

Motion and Kinematics

The

study

of

motion

without

regards

to

its

causes

is

called

kinematics

Important

topics

are

Displacement,

velocity,

and

acceleration

Freely

falling

objects

Projectile

motion

Newton’s Laws and Dynamics

The

study

of

motion

and

its

physical

causes

is

called

dynamics

Important

topics

are

Newton’s

laws

of

motion

Statics

and

equilibrium

Forces

of

friction

Energy and Work

Energy

is

one

of

the

most

important

concepts

in

science

and

is

present

in

a

variety

of

forms

Important

topics

are

Work

and

kinetic

energy

Potential

energy

Conservation

of

mechanical

energy

Power

Momentum and Collisions

The

concept

of

momentum

is

important

in

analyzing

multi
-
component

systems

Important

topics

are

Momentum

and

impulse

Elastic

and

inelastic

collisions

Rocket

propulsion

Newtonian Gravitation

Rotational

motion,

when

combined

with

Newton’s

law

of

universal

gravitation,

can

explain

certain

facts

space

travel,

satellite

motion,

and

the

motion

of

astronomical

objects
.

Rotational Dynamics

Rotational

dynamics

is

important

when

the

point

of

application

of

a

force

is

important
.

Important

topics

are

Torque

and

moment

of

inertia

Rotational

equilibrium

Rotational

kinetic

energy

Angular

momentum

Fluid Mechanics and Fluid Dynamics

An

understanding

of

the

fundamental

properties

of

fluids

is

important

in

all

the

sciences,

in

engineering,

and

in

medicine
.

Important

topics

are

Density

and

pressure

Buoyant

force

and

Archimedes’

principle

Bernoulli’s

equation

Poiseuille’s

law

Diffusion

Vibrations and Waves

Periodic

motion

(from

masses

on

springs

to

vibrations

of

atoms)

is

one

of

the

most

important

kinds

of

physical

behavior

and

cause

disturbances

that

move

through

a

medium

in

the

form

of

waves
.

Important

topics

are

Hooke’s

law

Simple

harmonic

motion

Properties

of

waves

Sound

Sound

waves

are

the

most

important

example

of

longitudinal

waves

and

examining

sound

waves

help

us

understand

how

we

hear
.

Important

topics

are

Properties

of

sound

Doppler

effect

Forced

vibrations

and

resonance

Thermal Physics

Thermal

physics

is

the

study

of

temperature

heat

and

how

they

affect

matter
.

Thermal

physics

requires

careful

definition

of

the

concepts

of

temperature,

heat,

and

internal

energy
.

Important

topics

Kinetic

theory

of

gases

Thermal

expansion

Latent

heat

and

internal

energy

Laws

of

thermodynamics

SI Units

The

basic

laws

of

physics

can

be

described

in

terms

of

fundamental

physical

quantities
.

In

mechanics,

all

physical

quantities

can

be

derived

by

length

(L),

mass

(M),

and

time

(T)
.

To

properly

communicate

the

result

of

a

measurement

of

a

certain

physical

quantity,

a

unit

for

the

quantity

must

be

defined
.

A

standard

system

of

units

for

the

fundamental

quantities

of

science

are

called

SI

units

(or

mks

units
)
.

SI Units

The

SI

units

for

length,

mass,

and

time

are

meter
,

kilogram
,

and

second
,

respectively
.

SI Units

The

SI

units

for

length,

mass,

and

time

are

meter
,

kilogram
,

and

second
,

respectively
.

Conversion of Units

Usually,

it’s

necessary

to

convert

units

from

one

system

to

another

by

using

conversion

factors
.

Conversion of Units

Ex
:

Convert

15

inches

to

centimeters

(cm)

and

meters

(m)
.

15

𝑖

2
.
54

𝑐
1

𝑖
=
38
.
1

𝑐

38
.
1

𝑐

0
.
01

1

𝑐
=
0
.
381

Conversion of Units

Ex
:

Convert

64
.
0

miles

per

hour

(mi/h)

to

meters

per

second

(m/s)
.

64
𝑖

1

3600



1
609

1

𝑖
=
28
.
60



Dimensional Analysis

In

physics,

dimension

denotes

the

physical

nature

of

a

quantity
.

Ex
:

Distance

has

the

dimensions

of

length

Brackets

will

be

used

to

denote

the

dimensions

of

a

physical

quantity

Ex
:

The

dimensions

of

volume

V

are

[V]

=

L
3

One

way

to

analyze

mathematical

expressions

that

relate

different

physical

quantities

is

through

dimensional

analysis

Dimensional Analysis

Dimensional

analysis

makes

use

of

the

fact

that

dimensions

can

be

treated

as

algebraic

quantities
.

In

order

for

any

equation

to

be

correct,

it

must

be

dimensionally

consistent
,

i
.
e
.

the

terms

on

the

opposite

side

of

an

equation

must

have

the

same

dimensions
.

Dimensional

analysis

is

a

quick

way

to

check

the

consistency

of

the

results

from

problem

solving
.

Dimensional Analysis

Ex
:

What

are

the

dimensions

for

velocity

v

and

acceleration

a
?

𝑣
=
𝐿
𝑇

𝑎
=
𝑣
𝑇
=
𝐿
/
𝑇
𝑇
=
𝐿
/
𝑇
2

Dimensional Analysis

Ex
:

Which

of

the

following

equations

are

dimensionally

consistent?

Assume

that

r

has

dimensions

of

length

=
1
2
𝑎

2

=
𝐿

𝑎

2
=
𝐿
𝑇
2

𝑇
2
=
𝐿

The

equation

is

dimensionally

consistent

Dimensional Analysis

Ex
:

Which

of

the

following

equations

are

dimensionally

consistent?

Assume

that

r

has

dimensions

of

length

𝑣
=
𝑎

2

𝑣
=
𝐿
𝑇

𝑎

2
=
𝐿
𝑇
2

𝑇
2
=
𝐿

The

equation

is

not

dimensionally

consistent

Dimensional Analysis

Ex
:

Which

of

the

following

equations

are

dimensionally

consistent?

Assume

that

r

has

dimensions

of

length

𝑎
=
𝑣
2
/

𝑎
=
𝐿
𝑇
2

𝑣
2

=
𝐿
2
/
𝑇
2
𝐿
=
𝐿
𝑇
2

The

equation

is

dimensionally

consistent

Dimensional Analysis

Ex
:

Which

of

the

following

equations

are

dimensionally

consistent?

Assume

that

r

has

dimensions

of

length

=
𝑣
2
/
𝑎

=
𝐿

𝑣
2
𝑎
=
𝐿
2
/
𝑇
2
𝐿
/
𝑇
2
=
𝐿

The

equation

is

not

dimensionally

consistent

Uncertainty and Significant Figures

In

practice,

we

use

significant

figures

to

convey

the

level

of

accuracy

associated

with

a

given

measurement
.

A

significant

figure

is

a

reliably

known

figure

(other

than

a

zero)

used

to

locate

a

decimal

point
.

In

calculations,

the

method

of

significant

figures

is

used

to

indicate

the

approximate

number

of

digits

that

should

be

retained

at

the

end

of

a

calculation
.

Uncertainty and Significant Figures

In

multiplying

(dividing)

2
+

quantities,

the

number

of

significant

figures

in

the

final

product

(quotient)

is

the

same

as

the

number

of

significant

figures

in

the

least

accurate

of

the

factors

being

combined
.

When

numbers

are

(subtracted),

the

number

of

decimal

places

in

the

results

should

equal

the

smallest

number

of

decimal

places

of

any

term

in

the

sum

(difference)
.

Scientific

notation

is

used

to

indicate

the

number

of

significant

figures

Significant Figures

Ex
:

A

rectangular

airstrip

measures

32
.
30

m

by

210

m

with

the

width

measured

more

accurately

than

the

length
.

Find

the

area,

taking

into

account

significant

figures
.

𝐴
=
𝐿


=
32
.
30

210

=
6
.
8

10
3

2

Significant Figures

Ex
:

The

edges

of

a

shoebox

are

measured

by

11
.
4

cm,

17
.
8

cm,

and

29

cm
.

Determine

the

volume

of

the

box

retaining

the

proper

number

of

significant

figures

in

your

.

=
𝐿



𝐻
=
11
.
4

𝑐

17
.
8

𝑐

29

𝑐
=
5
.
9

10
3
𝑐

3

Trigonometry

See

Appendix

A
.
5

and

section

1
.
7
-
1
.
8

in

your

textbook

for

a

quick

review

on

trigonometry
.

For

a

more

extensive

review,

see

the

following

:

http
:
//tutorial
.
math
.
lamar
.
ed
u/Extras/AlgebraTrigReview/
AlgebraTrigIntro
.
aspx