Unit Conversions and
Dimensional Analysis
Measurements in physics
- SI Standards (fundamental units)
Fundamental units:
length – meter (m)
time – second (s)
mass - kilogram (kg)
temperature - kelvin (K)
current – ampere (A)
luminous Intensity - candela (cd)
Amount of substance – mole (mol) – 6.02 x 1023
Derived units:
combinations of fundamental units
speed (v) = distance/time
units: m/s
acceleration (a) = velocity / time
units: m/s/s = m/s2
force (F) = mass x acceleration
units: kgm/s2 = N (Newton)
energy (E) = force x distance
units: kgm2/s2 = Nm = J (Joule)
charge (Q) = current x time
units: As = C (Coulomb)
1.3 The Role of Units in Problem Solving
THE CONVERSION OF UNITS
1 ft = 0.3048 m
1 mi = 1.609 km
1 hp = 746 W
1 liter = 10-3 m3
1.3 The Role of Units in Problem Solving
Example 1 The World’s Highest Waterfall
The highest waterfall in the world is Angel Falls in Venezuela,
with a total drop of 979.0 m. Express this drop in feet.
Since 3.281 feet = 1 meter, it follows that
(3.281 feet)/(1 meter) = 1
 3.281 feet 
Length  979.0 meters 
  3212 feet
 1 meter 
1.3 The Role of Units in Problem Solving
1.3 The Role of Units in Problem Solving
A typical bacterium has a mass of about 2.0 fg.
Express this measurement in terms of grams and
kilograms.
We know
1 fg = 10-15 g
and
1 kg = 103 g
 11015 g 
  2 1015 g
(2.0 fg ) 
 1 fg 
(2 10
15
 1kg 
18
  2.0 10 kg
g )
3
 110 g 
1.3 The Role of Units in Problem Solving
Reasoning Strategy: Converting Between Units
1. In all calculations, write down the units explicitly.
2. Treat all units as algebraic quantities. When
identical units are divided, they are eliminated
algebraically.
3. Use the conversion factors located on the page
facing the inside cover. Be guided by the fact that
multiplying or dividing an equation by a factor of 1
does not alter the equation.
1.3 The Role of Units in Problem Solving
Example 2 Interstate Speed Limit
Express the speed limit of 65 miles/hour in terms of meters/second.
Use 5280 feet = 1 mile and 3600 seconds = 1 hour and
3.281 feet = 1 meter.
feet
 miles 
 miles  5280 feet  1 hour 
Speed   65
1   65


 95
hour 
hour  mile  3600 s 
second


feet 
feet  1 meter 
meters


Speed   95
1   95

  29
second
 second 
 second  3.281 feet 
1.3 The Role of Units in Problem Solving
DIMENSIONAL ANALYSIS
[L] = length
[M] = mass
[T] = time
Is the following equation dimensionally correct?
x  vt
1
2
2
L 2
L   T  LT
T 
1.3 The Role of Units in Problem Solving
Is the following equation dimensionally correct?
x  vt
L
L   T  L
T 