Text book
Physics ; John D. Cutnell and Kenneth W.
Johnson; 7 th edition; Wiley; 2007.

The animation techniques used in the film Star Wars: Episode III —Revenge of the
Sith rely on computers and mathematical concepts such as trigonometry and vectors.
These mathematical tools will also be useful throughout this book in dealing with the laws of physics. (Lucasfilm/20th Century Fox/The Kobal Collection, Ltd.)

Length
Mass
Time
System
SI (International system)
Meter (m)
Kilogram (kg)
Second (s)
CGS
Centimeter (cm)
Gram (g)
Second (s)
BE (British
Engineering system)
Foot (ft)
Slug (sl)
Second (s)

• Originally, the distance measured along the earth’s surface between the north pole and the equator.
• Eventually, the meter became the distance between two marks on a bar of platinum –iridium alloy (
Figure ) kept at a temperature of 0
°C.
• Today, the meter is defined as the distance that light travels in a vacuum in a time of 1/299 792
458 second.
(The speed of light is a universal constant that is defined to be 299 792 458 m/s)

The standard platinum –iridium meter bar.
(Courtesy Bureau
International des Poids et Mesures, France)

• Originally, the kilogram was expressed in terms of a specific amount of water.
• Today, one kilogram is defined to be the mass of a standard cylinder of platinum –
iridium alloy, ( Figure 2 ).

The standard platinum –iridium kilogram is kept at the
International
Bureau of Weights and
Measures in Sévres, France.
This copy of the standard kilogram is housed at the
National Institute of Standards and Technology. (Sissy
Riley, Information Services
Division/National Inst of
Standards and Technology)

• Originally, the second was defined according to the average time for the earth to rotate once about its axis, one day being set equal to 86 400 seconds. The earth’s rotational motion was chosen because it is naturally repetitive, occurring over and over again.
• Today, we use the electromagnetic waves emitted by cesium-133 atoms in an atomic clock
like that in ( Figure 3 ). One second is defined as
the time needed for 9 192 631 770 wave cycles to occur.

This atomic clock, the
NIST-F1, is considered one of the world’s most accurate clocks.
It keeps time with an uncertainty of about one second in twenty million years.
(© Geoffrey Wheeler)

Prefix Symbol Factor tera
Giga
Mega
Kilo
Hecto
Deka deci centi milli micro nano pico femto
Prefix Symbol Factor
T
* G
M k h da d c m
μ n p f
Prefix Symbol Factor
10 12
10 9
10 6
10 3
10 2
10 1
10 -1
10 -2
10 -3
10 -6
10 -9
10 -12
10 -15

• Example: Body Mass Index (BMI)
The body mass index (BMI) takes into account your mass in kilograms (kg) and your height in meters (m) and is defined as follows:
BMI =

Mass
Height in in kg m

2
Determine the expression for the BMI of a person who has a mass of 180 lb. and a height of
71 in.
(1 kg corresponds to 2.205 lb, and 1 ft = 12 in.,
1 m = 3.281 ft.; 1 in. = 2.54 cm)

1 m
1 kg
X kg
2.205 lb
180 Ib
X = 81.6 kg
X m
3.281 ft 39.372 in.
71 in.
X = 1.8 m
MBI

81 .
6
 
2

25 .
1 kg / m
2
BMI (Kg/m 2 )
Below 18.5
18.5
–24.9
25.0
–29.9
30.0
–39.9
40 and above
Evaluation
Underweight
Normal
Overweight
Obese
Morbidly obese

• A scalar quantity is one that can be described with a single number
(including any units) giving its size or magnitude.
Examples: temperature, mass, volume, energy and time.
• A vector quantity is a quantity that deals inherently with both magnitude and direction .
• displacement vector, velocity, force, weight and acceleration.

A vector quantity has a magnitude and a direction.
The colored arrow in this drawing represents a displacement vector.

R

A

B

R

275 m , due east

125 m , due east

400 m , due east

R


R


A


B
 
2 
 
2
  tan

1
B
A

R

275 m , due east

125 m , due north
R


275 m

2 

125 m

2 
302 m
  tan

1


125 m
275 m



24 .
4 o north of east

( a) The displacement vector for a woman climbing 1.2 m up a ladder is . (b) The displacement vector for a woman climbing
1.2 m down a ladder is

D

A x
A y

A cos


A sin


• A displacement vector has a magnitude of r =
175 m and points at an angle of 50.0
° relative to the x axis in the figure. Find the x and y components of this vector .
x
 r cos
 y
 r sin
 


175 m


175 m
 
 cos sin
50 .
0 o
50 .
0 o



112

134 m m

• The figure shows three displacement vectors A , B , and C . These vectors are arranged in tail-to-head fashion, because they add together to give a resultant displacement R , which lies along the x axis. Note that the vector B is parallel to the x axis. What is the magnitude of the vector C?

A x
A y

A


B


C


R


B x
B y

C x

C y

R x

R y
A x
A y
R x
B
R
 y x


B y


20 m


20 m
 
 cos sin

10 m
 

10 m
 cos

60 .
0
60 .
0 sin
0 o
0 o o o







10 .
0
17 .
3
10 .
0
0 m m m m



35 .
0 m
 

35 .
0 m
 cos
 sin
0 o
0 o




35 .
0

0 m m
C
C x y


R
R x y


A
A x y


B
B x y


15 .
0 m

17 .
3 m
C

  

17 .
3

2
  tan

1

17 .
3
15

22 .
9 m
 
49 .
07 o south of east

• Are two vectors with the same magnitude necessarily equal? Give your reasoning.
• (a) Is it possible for one component of a vector to be zero, while the vector itself is not zero? (b) Is it possible for a vector to be zero, while one component of the vector is not zero? Explain.
• Can two nonzero perpendicular vectors be added together so their sum is zero?
Explain.

• Azelastine hydrochloride is an antihistamine nasal spray. A standard size container holds one fluid ounce ( oz ) of the liquid. You are searching for this medication in a European drugstore and are asked how many milliliters
(mL) there are in 1 oz . Using the following conversion factors, determine the number of milliliters in a volume of one fluid ounce:
1 gallon (gal) = 128 oz .;
3.785 x 10 -3 m 3 = 1 gal; 1 mL = 10 -6 m 3 .

• At a picnic, there is a contest in which hoses are used to shoot water at a beach ball from three directions. As a result, three forces act on the ball, F
1
, F
2
, and F
3
. Where F
1
= 50.0 N and F
2
= 90.0 N.
Determine (a) the magnitude of F
3 and (b) the angle θ such that the resultant force acting on the ball is zero.

• Vector A points along the + yaxis and has a magnitude of 100.0 units. Vector B points at an angle of 60.0
° above the + x axis and has a magnitude of 200.0 units.
Vector C points along the + x -axis and has a magnitude of 150.0 units. Which vector has (a) the largest x component and (b) the largest y component?

• Soccer player #1 is 8.6 m from the goal. If she kicks the ball directly into the net, the ball has a displacement labeled A . If, on the other hand, she first kicks it to player #2, who then kicks it into the net, the ball undergoes two successive displacements, A y and A x
. What are the magnitudes and directions of A x and A y
?