LECTURE 2
INTRODUCTION TO PHYSICS II
Instructor: Kazumi Tolich
Lecture 2
2
! 
Reading chapter 1-3 and 1-8
! 
Dimensional analysis
! 
Scientific notation
Conversion of units
Vectors and scalars
! 
! 
Dimension
3
! 
Dimension is the physical
nature of a quantity.
!  Dimension
"  feet,
of length, L
meters, inches, etc.
!  Dimension
of mass, M
"  kilograms,
!  Dimension
"  seconds,
tonne, slug, etc.
of time, T
hours, years, etc.
Dimensions of some common
physical quantities
Dimensional analysis
4
In dimensional analysis, dimensions are treated as
algebraic quantities.
!  Two quantities can be added or subtracted only if
they have the same dimensions.
!  The terms on both sides of an equation must have
the same dimensions.
! 
!  If
you have an equation, A = B + C, the dimensions of
A, B, and C must be the same.
Scientific notation
5
! 
Power of 10:
! 
! 
! 
! 
Multiplication and Division:
! 
! 
! 
1000 = 10 x 10 x 10 = 103
0.01 = 1 / 10 / 10 = 10-2
1 = 100
In multiplication, the exponents are added:
102 x 103 = 105
In division, the exponents are subtracted:
102 / 103 = 10-1
In scientific nation, a number is written as a product of a number between 1
(inclusive) and 10 (exclusive) times a power of 10.
! 
! 
3500 is 3.5 x 103
0.035 is 3.5 x 10-2
Prefixes for power of ten
6
“gigabytes”
“nanotechnology”
Conversion of units
7
! 
! 
Because different systems of units are in use, it is important to
know how to covert from one unit to another unit.
When physical quantities are added, subtracted, multiplied, or
divided in an algebraic equation, the unit can be treated like
any other algebraic quantity.
! 
Suppose you want to find the distance traveled in 3 hours (h) by a car
moving at a constant rate of 80 kilometers per hour (km/h). The distance
is the product of the speed v and the time t:
80 km
3 h = 240 km
h
! 
We cancel the unit of time, the hours, just as we would any algebraic
quantity to obtain the distance in the proper unit of length, the kilometer.
Conversion of units: 2
8
!  Suppose
we want to convert the units in our answer
from kilometers (km) to miles (mi).
!  1 mi = 1.609 km, so the conversion factor is
1 mile
=1
1.609 km
!  Because
any quantity can be multiplied by 1 without
changing its value,
240 km = 240 km × 1 = 240 km
1 mile
= 149 mile
1.609 km
Example: 1
9
! 
Your employer sends you on a trip to a foreign
country where the road signs give distances in
kilometers, and the automobile speedometers are
calibrated in kilometers per hour. If you drive
90 km/h, how fast are you going
a) 
b) 
in meters per second and
in miles per hour?
Example: 2
10
! 
A liter (L) is the volume of a cube that is 10 cm by
10 cm by 10 cm. If you drink 1 L (exact) of water,
how much volume in cubic centimeters and in cubic
meters would it occupy in your stomach?
Example: 3
11
! 
Mary is driving in a straight line at
60.00 miles/hour. Nate is driving at a velocity
2500 µm/ms slower than Mary in the same
direction. How fast is Nate driving in m/s?
Express the answer in scientific notation.
Order of magnitude calculations
12
! 
In doing rough calculations, or order-of-magnitude
calculations, we sometimes round off a number to
the nearest power of 10.
height of an ant might be 8 × 10-4 m or
approximately 10-3 m. The order of magnitude of an
ant's height is 10-3 m.
!  The average height of men in the US is about 1.8 m. It
is in the order of magnitude of 100 m, or 1 m.
!  The
The universe by orders of magnitude
13
Example: 4
14
! 
What thickness of rubber tread is worn off the tire
of your automobile as it travels 1 km (0.6 mi)?
Example: 5
15
! 
Estimate the number of grains of sand on a beach.
Vector and scalar quantities
16
! 
A vector quantity has a magnitude and direction.
! 
! 
! 
! 
! 
Displacement (m): how far something moved in what direction
Velocity (m/s): how fast something is moving in what direction
Acceleration (m/s2): how fast velocity is changing in what direction
etc.
A scalar quantity has only magnitude.
! 
! 
! 
! 
Time (s): how long it has been.
Temperature (K): how hot something is.
Mass (kg): how much stuff there is.
etc.