This document contains a summary of the first lecture in an introductory physics course. The lecture covered the following key points: - Physics aims to study and express the fundamental laws of nature mathematically through equations. Most physical quantities have standardized units. - The International System of Units (SI) defines the base units of the meter (length), kilogram (mass), and second (time). Other units are derived from these base units. - Vectors represent quantities that have both magnitude and direction, while scalars only have magnitude. Problem solving in physics involves identifying relevant equations and checking solutions.

1. Physics - Mechanics
Lecture 1
Introduction to Physics
September 2, 2013

2. Lecture 1 2/212/21
Physics and the Laws of Nature
Physics: the study of the fundamental
laws of nature.
● These laws can be expressed as
mathematical equations. (e.g., F = m a)
● Most physical quantities have units,
which must match on both sides of an
equation.
● Much complexity can arise from even
relatively simple physical laws.

3. Lecture 1 3/21
Units
With a few exceptions, all physical quantities have
units. Examples:
Mass - kilograms (kg)
Speed - meters per second (m/s)
Pressure - pascals (P)
Energy - joules (J)
Electric Potential - volts (V)
Rather surprisingly, the units of almost all physical
quantities can be expressed as combinations of only
the units for mass, length, and time, i.e., kilograms,
meters, and seconds. A few physical quantities (e.g.,
index of refraction) are pure numbers that have no
associated units.

4. Lecture 1 4/21
Standard International Units
Standard International (SI) Units (also known as MKS)
• Length: meter m
• Mass: kilogram kg
• Time: second s
Unit Conversions
1 in = 2.54 cm 1 cm = 0.3937 in
1 mi = 1.609 km 1 km = 0.621 mi
1 mph = 0.447 m/s 1 m/s = 2.24 mph
Note:
The English pound unit is a measure of force or weight, not mass.
A kilogram of mass has a weight of 2.2046 pounds at standard gravity, but
will have slightly different weights at different locations on the Earth (poles,
equator).
}English Units
(Used only in USA, Liberia,
and Myanmar)
Units for almost all other physical quantities can be constructed from
mass, length, and time, so these are the fundamental units.

5. Lecture 1 5/21
The SI Time Unit: second (s)
The second was originally defined as (1/60)(1/60)(1/24) of a mean solar day.
Currently, 1 second is defined as 9,192,631,770 oscillations of the radio
waves absorbed by a vapor of cesium-133 atoms. This is a definition that can be
used and checked in any laboratory to great precision.
13th
Century Water Clock Cesium Fountain Clock

6. Lecture 1 6/21
The SI Length Unit: meter (m)
The meter was originally defined
as 1/10,000,000 of the distance from
the Earth’s equator to its North pole
on the line of longitude that passes
through Paris. For some time, it was
defined as the distance between two
scratches on a particular platinum-
iridium bar located in Paris.
Currently, 1 meter is defined as the
distance traveled by light in
1/299,792,458 of a second

7. Lecture 1 7/21
The SI Mass Unit: kilogram (kg)
The kilogram was originally defined
as the mass of 1 liter of water at 4o
C.
Currently, 1 kilogram is the mass of
the international standard kilogram, a
polished platinum-iridium cylinder
stored in Sèveres, France. (It is
currently the only SI unit defined by a
manufactured object.)
Question: In a “telephone”
conversation, could you accurately
describe to a member of a alien
civilization how big a kilogram was?
Answer: More or less. Avagadro’s
number of carbon-12 atoms
(6.02214199… x 1023
) has a mass of
exactly 12.00000000000… grams.

8. Lecture 1 8/21
Prefixes

9. Lecture 1 9/21
Dimensions and Units

10. Lecture 1 10/21
Any valid physical equation must be dimensionally
consistent – each side must have the same dimensions.
From the Table:
Distance = velocity × time
Velocity = acceleration ×
time
Energy = mass × (velocity)2
Dimensional Analysis (1)

11. Lecture 1 11/21
Dimensional Analysis (2)
The periodThe period PP (T)(T) of a swingingof a swinging
pendulum depends only on the lengthpendulum depends only on the length
of the pendulumof the pendulum dd (L)(L) and theand the
acceleration of gravityacceleration of gravity gg (L/T(L/T22
))..
Which of the following formulas forWhich of the following formulas for PP
couldcould be correct ?be correct ?
P
d
g
= 2πP
d
g
= 2π(a)(a) (b)(b) (c)(c)P = 2π (dg)2
ExampleExample::

12. Lecture 1 12/21
L
L
T
L
T
T⋅





 = ≠2
2 4
4
Dimensional Analysis (3)
L
L
T
T T
2
2
= ≠
Remember that P is in units of time (TT), d is
length (L) and g is acceleration (L/T2
).
The both sides must have the same units
( )P dg= 2
2
π(a)(a) (b)(b) (c)(c)P
d
g
= 2π
Try equation (a). Try equation (b). Try equation (c).
TT
T
L
L 2
2
==
P
d
g
= 2π

13. Lecture 1 13/21
Some Approximate Magnitudes

14. Lecture 1 14/21
Order of Magnitude Calculations
1. Make a rough estimate of the relevant quantities
to one significant figure, preferably some power of 10.
2. Combine the quantities to make the estimate.
3. Think hard about whether the estimate is reasonable.
Example:
How fast does an Olympic sprinter cross the finish
line in the 100 m dash?
Analysis:
Typical 100 m dash time is ~10 s, so average speed is
about 10 m/s. Sprinters “kick” near the finish line, so
speed there is faster. 50% faster? Maybe. That would
mean the finish-line speed is ~15 m/s. Reasonable? Yes.

15. Lecture 1 15/21
Example: Burning Rubber
Problem:
When you drive your car 1 km, estimate the
thickness of tire tread that is worn off.
Answer:
1. Estimate the distance require to wear down a
tire tread to the point where it needs to be
replaced: ~60,000 km (or 37,000 miles)
2. Estimate the thickness of a typical tire tread
lost on a worn tire: ~ 1 cm.
3. Consider the following ratio:
5
71 cm of tread loss 1.67 10 cm of tread loss
2 10 m of tread loss per km
60,000 km of travel 1 km of travel
−
−×
= ≈ ×
Therefore, a car loses about 2x10-7
m = 0.2 µm of tire tread in
driving 1 km.

16. Lecture 1 16/21
Problem Solving in Physics
No recipe or plug-and-chug works all the time,
but here are some guidelines:
1. Read the problem carefully.
2. Draw a sketch of the system.
3. Visualize the physical process involved.
4. Devise a strategy for solving the problem.
5. Identify the appropriate equations.
6. Solve the equations. Calculate the answer.
7.Check your answer. Dimensions? Reasonable?
8.Explore the limits and special cases.

17. Lecture 1 17/21
Scalars and Vectors
Temperature = Scalar
Quantity is specified by a single
number giving its magnitude.
Velocity = Vector
Quantity is specified by
three numbers that give
its magnitude and direction
(or its components in three
perpendicular directions).

18. Lecture 1 18/21
Properties of Vectors

19. End of Lecture 1
 Before the Thursday lecture, read
Walker, Chapter 2.1 through 2.3.
 Obtain a HiTT clicker from the
University Bookstore. We will use soon.
 Lecture Homework #1 has been posted
on the WebAssign system and is due at or
before 11:59 PM on Thursday, Jan. 12, i. e.,
on Thursday of next week.