Welcome to Caltech!
and
Physics 1a:
Newtonian mechanics
Lecture 1: Introduction
Basic info
Ryan Patterson, rbpatter@caltech.edu
Office: Lauritsen 339, x5753
Lectures:
Wed and Fri, 11am
201 E. Bridge (a.k.a. Feynman Lecture Hall)
Sections:
Mon and Thu, 1pm or 3pm, various locations
and instructors.
Office hours:
Various times, locations, and instructors
(see webpage)
Course webpage
http://www.its.caltech.edu/~tmu/ph1a/
Course webpage
http://www.its.caltech.edu/~tmu/ph1a/
Past quiz and final exam problems
(many assigned as homework)
General information
Lecture notes,
quizzes, and
other documents
Course calendar
On the course webpage…
Required reading
Homework assignments
Quizzes
Table from last page
of PDF syllabus.
Check there for updates.
Material overview
All of this in
Introduction
about 9 weeks
1D motion
Falling bodies, acceleration
Reference frames, 2D motion
Newton's laws
Forces of nature
Circular motion
Non-inertial frames
Energy
Linear momentum
Angular Momentum
Rotational dynamics
Oscillatory motion
Orbits, Kepler's laws
Fluid Mechanics
Gyroscopes
Material overview
A lot will be covered in a
short amount of time.
All of this in
Introduction
about 9 weeks
1D motion
Some things may seem hard;
Falling bodies, acceleration
some easy. Stay on your toes!
Reference frames, 2D motion
Take advantage of:
Newton's laws
Reading, Lectures, Sections
Forces of nature
and
Circular motion
Office hours, Core study sessions
Non-inertial frames
Energy
Office hours
Linear momentum
Times (typically on Tuesday) and locations
are listed on the course webpage (some still
Angular Momentum
to be filled in)
Rotational dynamics
Oscillatory motion
Core study sessions
This is a new thing this year! Undergraduate
Orbits, Kepler's laws
tutors will be on hand Monday 8pm – 11pm
Fluid Mechanics
on the 9th floor of Millikan. (Monday is
Gyroscopes
physics. Other subjects are on others days.)
http://xkcd.com/435/
http://xkcd.com/435/
Figuring out how
the universe works
http://xkcd.com/435/
Figuring out how
the universe works
- The primary material in this course is about three centuries old.
- But, one has to begin at the beginning…
Ph 1
Ph 1
Engineering Biology Geosciences
Chemistry
Physics
etc…
Astronomy
Ph 1
Essential math
We will need these tools right out of the gate.
Some calculus
 notation
 differentiation
 sum rule, product rule, etc.
 integration
 finding minima and maxima
Vectors
 notation
 components, magnitudes
 algebraic manipulations
 dot product, projections
 cross product
 unit vectors
The first set of required reading
is longer than usual because it
includes reviewing these topics
(Chapters 3 and 5).
Even if it’s just to shake the
rust off, you should review
this material!
SI units
Stay consistent ⇒ less work & fewer mistakes
length : meter (m)
time
: second (s)
mass : kilogram (kg)
Fundamental SI units
SI units
Stay consistent ⇒ less work & fewer mistakes
length : meter (m)
time
: second (s)
mass : kilogram (kg)
velocity : m/s
accel. : m/s2
area
: m2
etc…
Fundamental SI units
Derived SI units
SI units
Stay consistent ⇒ less work & fewer mistakes
length : meter (m)
time
: second (s)
mass : kilogram (kg)
velocity : m/s
accel. : m/s2
area
: m2
etc…
force : newton (N) = kg∙m/s2
energy : joule (J) = kg∙m2/s2
etc…
Fundamental SI units
Derived SI units
Derived SI units
with special names
Converting units
Consider a velocity:
v = 88 mph =
88 mi
1 hr
If we want m/s units, multiply by “1” repeatedly…
88 mi  1 hr  1609 m
v=
1 hr
3600 s
1 mi
=1
=1
m
= 39.3 s
Checking your work with units
Q: How tall is Bob?
Checking your work with units
Q: How tall is Bob?
(work, work, algebra, algebra, …)
Checking your work with units
Q: How tall is Bob?
(work, work, algebra, algebra, …)
A: 8 kg
← Clearly a bad answer! Look for the error.
Checking your work with units
Q: How tall is Bob?
(work, work, algebra, algebra, …)
A: 8 kg
← Clearly a bad answer! Look for the error.
A: 92 m ← Right units, but physically questionable...
Checking your work with units
Q: How tall is Bob?
(work, work, algebra, algebra, …)
A: 8 kg
← Clearly a bad answer! Look for the error.
A: 92 m ← Right units, but physically questionable...
A: 1.8 m ← Could possibly be correct.
Checking your work with units
Q: How tall is Bob?
(work, work, algebra, algebra, …)
A: 8 kg
← Clearly a bad answer! Look for the error.
A: 92 m ← Right units, but physically questionable...
A: 1.8 m ← Could possibly be correct.
Mistakes of the first type should never survive!
Algebra gone awry?
Consider:
Distances x and y
Time t
Algebra gone awry?
Consider:
Distances x and y
Time t
x+t
= nonsense
[ 4 m + 2 s = ??? ]
Algebra gone awry?
Consider:
Distances x and y
Time t
x+t
= nonsense
[ 4 m + 2 s = ??? ]
cos(xy) = nonsense
[ cos(9 m2) = ??? ]
Algebra gone awry?
Consider:
Distances x and y
Time t
x+t
= nonsense
[ 4 m + 2 s = ??? ]
cos(xy) = nonsense
[ cos(9 m2) = ??? ]
log(x/y) = okay!
[ log(unitless number) ]
Algebra gone awry?
Consider:
Distances x and y
Time t
x+t
= nonsense
[ 4 m + 2 s = ??? ]
cos(xy) = nonsense
[ cos(9 m2) = ??? ]
log(x/y) = okay!
[ log(unitless number) ]
Similarly:
Consider the area of a rectangle with sides 2 m and 4 m
A=24=8
A = (2 m)  (4 m) = 8 m2
G. I. Taylor used pictures
like these to estimate the
(then still classified) yield
of the Trinity nuclear
device.
Early in the explosion, the radius R
of the blast depends only on:
E = energy released (i.e., the yield)
t = time since detonation
𝜌 = density of air
Time standard
1 second  period of that pendulum ?
 not a great global standard
Time standard
1 second  period of that pendulum ?
 not a great global standard
1 second  (Earth’s rotation period) / 86400 ?
 rotation period varies a lot (seasons, earthquakes, long-term wobbles)
Time standard
1 second  period of that pendulum ?
 not a great global standard
1 second  (Earth’s rotation period) / 86400 ?
 rotation period varies a lot (seasons, earthquakes, long-term wobbles)
1 second  9,192,631,770 periods of the radiation corresponding to the transition
between the two hyperfine levels of the ground state of 133Cs.
 very stable, very reproducible!
Cesium-133
energy levels
Compare clock rates at two heights differing by only 33 cm.
At the higher position, the observed rate is higher by a factor of
1.00000000000000004.
seconds
1018
1015
1012
109
106
103
100
10-3
10-6
10-9
10-12
10-15
10-18
10-21
10-24
10-27
10-30
10-33
10-36
10-39
10-42
10-45
1 yr
1s
range of direct
human experience
age of universe
Light from the early universe,
showing up as microwaves today
seconds
ESA/Planck
1018
1015
1012
109
106
103
100
10-3
10-6
10-9
10-12
10-15
10-18
10-21
10-24
10-27
10-30
10-33
10-36
10-39
10-42
10-45
age of earth
1 yr
1s
range of direct
human experience
seconds
age of universe
Super Kamiokande detector, Japan
1018
1015
1012
109
106
103
100
10-3
10-6
10-9
10-12
10-15
10-18
10-21
10-24
10-27
10-30
10-33
10-36
10-39
10-42
10-45
age of earth
1 yr
1s
lower limit on proton
lifetime (1041 s)
range of direct
human experience
seconds
age of universe
time since Cretaceous-Tertiary event
1018
1015
1012
109
106
103
100
10-3
10-6
10-9
10-12
10-15
10-18
10-21
10-24
10-27
10-30
10-33
10-36
10-39
10-42
10-45
age of earth
1 yr
1s
lower limit on proton
lifetime (1041 s)
range of direct
human experience
seconds
age of universe
time since Cretaceous-Tertiary event
1018
1015
1012
109
106
103
100
10-3
10-6
10-9
10-12
10-15
10-18
10-21
10-24
10-27
10-30
10-33
10-36
10-39
10-42
10-45
age of earth
lower limit on proton
lifetime (1041 s)
time since first humans
1 yr
1s
range of direct
human experience
age of universe
time since Cretaceous-Tertiary event
duration of this lecture
seconds
blink of an eye
1018
1015
1012
109
106
103
100
10-3
10-6
10-9
10-12
10-15
10-18
10-21
10-24
10-27
10-30
10-33
10-36
10-39
10-42
10-45
age of earth
lower limit on proton
lifetime (1041 s)
time since first humans
1 yr
1s
range of direct
human experience
age of universe
time since Cretaceous-Tertiary event
duration of this lecture
seconds
blink of an eye
shortest controlled laser pulse
1018
1015
1012
109
106
103
100
10-3
10-6
10-9
10-12
10-15
10-18
10-21
10-24
10-27
10-30
10-33
10-36
10-39
10-42
10-45
age of earth
lower limit on proton
lifetime (1041 s)
time since first humans
1 yr
1s
range of direct
human experience
age of universe
time since Cretaceous-Tertiary event
duration of this lecture
seconds
blink of an eye
shortest controlled laser pulse
1018
1015
1012
109
106
103
100
10-3
10-6
10-9
10-12
10-15
10-18
10-21
10-24
10-27
10-30
10-33
10-36
10-39
10-42
10-45
age of earth
lower limit on proton
lifetime (1041 s)
time since first humans
1 yr
range of direct
human experience
1s
lifetime of charged pion (“weak” decay)
lifetime of neutral pion (“EM” decay)
lifetime of  particle (“strong” decay)
age of universe
time since Cretaceous-Tertiary event
duration of this lecture
seconds
blink of an eye
shortest controlled laser pulse
Planck time
1018
1015
1012
109
106
103
100
10-3
10-6
10-9
10-12
10-15
10-18
10-21
10-24
10-27
10-30
10-33
10-36
10-39
10-42
10-45
age of earth
lower limit on proton
lifetime (1041 s)
time since first humans
1 yr
range of direct
human experience
1s
lifetime of charged pion (“weak” decay)
lifetime of neutral pion (“EM” decay)
lifetime of  particle (“strong” decay)
Distance standard
1 meter  the distance that light travels in 1/(299,792,458) seconds (in a vacuum)
Means that the speed of light is given exactly by:
c = 299,792,458 m/s
Distance standard
1 meter  the distance that light travels in 1/(299,792,458) seconds (in a vacuum)
Means that the speed of light is given exactly by:
c = 299,792,458 m/s
Mass standard
1 kilogram  the mass of this thing
Work is ongoing to replace this standard
with something more “natural”,
possibly based on Planck’s constant ℏ.
(digital clock demo, part 2…)
Next time
We’ll get into the thick of it…
- Position, velocity, acceleration
- Constant acceleration
- Objects in freefall
- Reference frames
- 2D motion, trajectories