Storyline
Chapter 1:
Physics and Measurement
Standards of
Length, Mass, and Time
Standards in measurement must:
• be readily accessible
• possess some property that can be measured reliably
• yield same result
• not change with time
In 1960, an international committee established a set of standards for the
fundamental quantities of science: SI (Système International)
Base Units or Fundamental units
• Length (m, meter)
• Mass (kg, kilogram)
• Time (s, second)
• Temperature (K, kelvin)
• Electric current (A, ampere)
• Luminous intensity (cd, candela)
• Amount of substance (mol, mole)
Length
Length: distance between two points in space
Meter: distance traveled by light in vacuum during a time interval of
1/299 792 458 second
Mass
Kilogram: mass of a specific platinum–
iridium alloy cylinder kept at the
International Bureau of Weights and
Measures at Sèvres, France
Time
Second: 9 192 631 770 times the period of
vibration of radiation from the cesium-133 atom
Powers of 10
Dimensions
In physics: dimension denotes the physical nature
of a quantity
Use brackets [ ] to denote dimensions of a physical quantity
Base Quantities: [Length] = L, [Mass] = M, [Time] = T
Derived Quantities: area [A] = L2, speed [v] = L/T
Dimensional Analysis
An equation must be dimensionally (unit) consistent.
Example:
1
1. Show the following equation 𝑥𝑥 = 𝑎𝑎𝑡𝑡 2 dimensionally consistent,
2
where a is acceleration and t is time.
𝐿𝐿
𝑚𝑚
Solution: 𝐿𝐿 = 2 � 𝑇𝑇 2 = 𝐿𝐿
or 𝑚𝑚 = 2 � 𝑠𝑠 2 = 𝑚𝑚
𝑇𝑇
𝑠𝑠
2. The equation for the change of position of a particle starting at x
= 0 m is given by x = bt + ct4 . If [x] = m and [t] = s, what are units of
b and c?
Solution:
[x] = m  [bt] = m  [b][t] = m  [b] = m/[t] = m/s.
[x] = m  [ct4] = m  [c][t4] = m 
[c] = m/[t4] = m/s4.
Quick Quiz
True or False: Dimensional analysis can give
you the numerical value of constants of
proportionality that may appear in an
algebraic expression.
Key: Quick Quiz Key
True or False: Dimensional analysis can give
you the numerical value of constants of
proportionality that may appear in an
algebraic expression.
False
Example :
Analysis of an Equation
Show that the expression v = at, where v represents
speed, a acceleration, and t an instant of time, is
dimensionally correct.
Left side of equation:
Right side of equation:
L
𝑣𝑣 =
T
L
L
𝑎𝑎𝑎𝑎 = 2 T =
T
T
Therefore, v = at is dimensionally correct because we have
the same dimensions on both sides.
Conversion of Units
1 mi = 1 609 m = 1.609 km
1 ft = 0.304 8 m = 30.48 cm
1 m = 39.37 in. = 3.281 ft
1 in. = 0.025 4 m
= 2.54 cm exactly
1 lb = 4.448 N
1 mi/h = 0.447 m/s = 1.61 km/h
Conversion of Units: Samples
Examples:
A. Convert 15.0 in. to centimeters.
cm
Solution: 1 in. = 2.54 cm →
1 in.
2.54 cm
 15.0 in. = 15.0in.
= 𝟑𝟑𝟑𝟑. 𝟏𝟏 cm
1in.
2.54
B. Convert 170 lb in N and 90 mil/h in m/s.
Solution:
Using conversion factor: 1 lb = 4.448 N
 170 lb = 170 x4.448 N = 756 N
Using conversion factor: 1 mil/h = 0.447 m/s
 90 mil/h = 90 x 0.447 m/s = 40.2 m/s
Quick Quiz: mi and km
The distance between two cities is 100 mi.
What is the number of kilometers between the
two cities?
(a) smaller than 100
(b) larger than 100
(c) equal to 100
Key: Quick Quiz
The distance between two cities is 100 mi.
What is the number of kilometers between the
two cities?
(a) smaller than 100
(b)larger than 100
(c) equal to 100
Example :
Is He Speeding?
On an interstate highway in a rural region of Wyoming,
a car is traveling at a speed of 38.0 m/s. Is the driver
exceeding the speed limit of 75.0 mi/h?
38.0 m/s
1 mi
1609 m
60 s
1min
60min
= 85.0 mi/h
1h
Yes, he is speeding!
Example :
Is He Speeding?
What if the driver were from outside the United States
and is familiar with speeds measured in kilometers per
hour? What is the speed of the car in km/h?
mi 1.609 km
85.0
h
1mi
= 137 km/h
Significant Figures:
Scientific Notation
1500 g →? significant figures
1.500 × 103 g → 4 significant figures
1.50 × 103 g → 3 significant figures
1.5 × 102 g → 2 significant figures
2.3 × 10−4 → 2 significant figures → 0.00023
2.30 × 10−4 → 3 significant figures → 0.000230
Significant Figures:
Multiplying Rule
When multiplying several quantities, the number of
significant figures in the final answer is the same as
the number of significant figures in the quantity
having the smallest number of significant figures. The
same rule applies to division.
Example:
23.2 x 5.174 = 1.20 x 102
23.2/5.174 = 4.48
1.327 x 2.8 = 3.7
Significant Figures: Adding Rule
When numbers are added or subtracted, the number of decimal
places in the result should equal the smallest number of
decimal places of any term in the sum or difference.
23.2 + 5.174 = 28.374
→ 23.2 has one decimal place → sum = 28.4
1.0001 + 0.0003 = 1.0004
1.002 − 0.998 = 0.004
Significant Figures
6.0 ± 0.1 cm
Example: Samples
Significant Figures
Example:
A. Find area of Blu-Ray Disc
Equation for area of circle given 𝐴𝐴 = 𝜋𝜋𝑟𝑟 2
Calculate and keep two significant figures, since radius
only has two significant figures:
𝐴𝐴 = 𝜋𝜋𝑟𝑟 2 = 𝜋𝜋[6.0 cm ]2 = 𝟏𝟏. 𝟏𝟏 × 𝟏𝟏𝟎𝟎𝟐𝟐 𝐜𝐜m𝟐𝟐
B. What is the answer with the correct number of
significant figures to the following calculation:
2.12 × 3.232 - 5.1?
Keep 3 significant figure: 2.12 × 3.232=6.85
Keep lease decimal: 2.12 × 3.232 - 5.1 = 6.85 – 5.1 = 1.8
Three Significant Figures
In this book, most of the numerical examples and end-ofchapter problems will yield answers having three significant
figures. When carrying out estimation calculations, we shall
typically work with a single significant figure.
last digit dropped > 5: increase last retained digit by 1:
1.356 → 1.36
last digit dropped = 5: increase last retained rounded to
nearest even number: 1.345 → 1.34
last digit dropped < 5: leave last retained as is: 1.343 →
1.34
Example :
Installing a Carpet
A carpet is to be installed in a rectangular room whose
length is measured to be 12.71 m and whose width is
measured to be 3.46 m. Find the area of the room.
12.71 m × 3.46 m = 43.9766 m2
3.46 → 3 sig figs → 𝑨𝑨 = 𝟒𝟒𝟒𝟒. 𝟎𝟎 m𝟐𝟐
Summary of Units
Base Units in SI (Système
International): Length (m, meter, L)
Mass (kg, kilogram, M)
Time (s, second, T)
Derived Units in SI: Velocity (m/s, L/T)
Acceleration (m/s2, L/T2)
Special Name in SI: Force (N, Newton)
Energy (J, Joules)
Power (W, Watts)
An equation must be dimensionally
(unit) consistent.
Conversion of Units: 1 mil = 1609 m,
1in = 2.54 cm, 1 lb = 4.448 N
When multiplying several quantities,
the number of significant figures in
the final answer is the same as the
number of significant figures in the
quantity having the smallest number
of significant figures. The same rule
applies to division.
Ex. 23.2 x 5.174 = 1.20 x 102
When numbers are added or
subtracted, the number of decimal
places in the result should equal the
smallest number of decimal places of
any term in the sum or difference.
Ex. 23.21 + 5.1741 = 28.38