Transcript Dimensions & Unit Conversions

Dimensions & Unit
Conversions
August 11 / 12, 2014
Dimensions & Units

All physical quantities have dimensions and are
expressed in units.
 Dimension describes what the physical quantity is
 Units are how the quantity is measured
Example: Speed
Speed has the dimensions of Length / Time
Speed may be measured by a variety of different units
(e.g. mph, km/s, etc.)
You can convert between different units of the same physical
quantity (e.g. seconds into hours) but CANNOT convert one
dimension into another (e.g you can’t convert time into length)
In the study of mechanics, we will work with physical quantities that
can be described in terms of three dimensions:
length (L), time (T) , and mass (M).
The corresponding basic SI- units are:
Length – 1 meter (1m) is the distance traveled by the light in a
vacuum during a time of 1/299,792,458 second.
Mass – 1 kilogram (1 kg) is defined as a mass of a specific
platinum-iridium alloy cylinder kept at the International Bureau of
Weights and Measures at Sevres, France
Time – 1 second (1s) is defined as 9,192,631,770 times the period
of oscillation of radiation from the cesium atom.
ALL physical dimensions can be expressed in terms of combinations
of seven basic dimensions, which can be measured directly.
Derived dimensions are combinations of 7 basic ones.
Basic
Physical
Quantity
Basic
Dimension
Distance,
height,width
Length (L)
Mass (m)
Mass (M)
Basic
SI Unit
meter (m)
kilogram
(kg)
Time (t)
Time (T)
second (s)
Electric
Current (I)
Electric
Current (I)
ampere (A)
Temperature
Temperature
kelvin (K)
Amount of
matter
Amount of
matter
mole
Intensity of
light
Intensity of
light
candela
(cd)
Derived
Physical
Quantity
Derived
Dimension
Derived
SI Unit
area
L2
m2
Volume
L3
m3
speed
L/T
m/s
acceleration
L/T2
m/s2
ML/T2
kg.m/s2
newton (N)
force
power
density
M L2/T3
M/
L3
kg.m2/s3
watt (W)
kg/m3
Go back to the measurements you did earlier
& fill in the rest of the table
Quantity Measurement
measured
Dimensions
Units
SI or not?
base unit
femto
f
pico
nano
p
n
m
10-15
10-12
10-9
10-6
Smaller units
micro
mili
1
m
10-3
100
centi
deci
c
10-2
d
10-1
kilo
mega
giga
tera
k
M
G
T
103
106
109
1012
Larger units
every step is 10± 1 power
They are grouped into steps 10± 3
f
p
n
m
10-15
10-12
10-9
10-6
1
m
10-3
c
10-2
100
d
10-1
k
M
G
T
103
106
109
1012
SI conversions!
larger unit →
smaller number
5 𝑚ℓ = _______ 𝑘ℓ
The problem: We have to convert 5 into kl.
Will the number in front of kl be smaller or bigger?
Smaller!!
p
f
10-15
n
m
m
1
k
M
G
Moving the decimal seems so much easier … why do we both
-3
0
conversion
10-12
10-9
10-6 with10
10factors?
103
106
109
c
d
Because sometimes moving
10-2the decimal
10-1 won’t work … more on
this later!
SI conversions!
larger unit →
smaller number
5 𝑚ℓ = _______ 𝑘ℓ
1012
We can do SI unit conversions in two different
methods:
=1
1𝑘ℓ
5 𝑚ℓ = 5 𝑚ℓ ×
= 5 × 10−6 𝑘ℓ
6
10 𝑚ℓ
Method 1: Conversion factors
* Note: The larger unit always has a 1 in the conversion factor (i.e. 1 kℓ and 1 km).
5𝑚ℓ =
T
6 𝑠𝑡𝑒𝑝𝑠 𝑡𝑜 𝑡ℎ𝑒 𝑟𝑖𝑔ℎ𝑡
= 5 × 10−6 𝑘ℓ
0.000005
Method 2: Moving the decimal
f
p
n
m
10-15
10-12
10-9
10-6
1
m
10-3
c
10-2
100
d
10-1
k
M
G
T
103
106
109
1012
Another problem!
smaller unit →
bigger number
Will the number in front of cm be smaller or bigger?
larger!!
5 𝑘𝑚 = _______ 𝑐𝑚
=1
105 𝑐𝑚
5 𝑘𝑚 = 5𝑘𝑚 ×
= 5 × 105 𝑐𝑚
1𝑘𝑚
5𝑘𝑚 =
5 𝑠𝑡𝑒𝑝𝑠 𝑡𝑜 𝑡ℎ𝑒 𝑙𝑒𝑓𝑡
= 5 × 105 𝑐𝑚
500000 𝑐𝑚
Method 1: Conversion factors
Method 2: Moving the decimals
One more as a class …
The wavelength of green light is 500 nm.
How many meters is this?
1𝑚
500 𝑛𝑚 ×
= 500 × 10−9 𝑚 = 5 × 10−7 𝑚
9
10 𝑛𝑚
or
500 𝑛𝑚 = 0.0000005 𝑚 = 5 × 10−7 𝑚
Practice using both methods
on your whiteboard …
hold it up when you are done
I have 906 gigabyte hard drive on my computer.
How many bytes of data will it hold?
9.06 X 1010 bytes
Now practice more.
If you are confident, do them by yourself.
If you are not confident, then work with someone who is confident.
BUT, the less confident one should be the one leading the practice
and talking out their process!!!!
Practice 1: Basic SI conversions
1.
2.
3.
4.
How many liters is 16 𝜇ℓ ? 16 𝜇ℓ = 1.6 × 10−5 ℓ
4.3 x 104 ns = ? µs 4.3× 104 𝑛𝑠 = 43 µs
5.2 x 108 ms = ? Ks 5.2 × 108 𝑚𝑠 = 520 𝑘𝑠
0.09 𝑐𝑚 = 9 𝑋 105 pm
0.09 cm = ? pm
When do you need to use
conversion factors?
When converting between SI and English units
 When converting between units that have
exponents

Example 1: 20 m/s → km/h
20
𝑚
𝑠
𝑚 1 𝑘𝑚
= 20
𝑠 103 𝑚
Example 2: 7.2 m3 → mm33
7.2 𝑚3 = 7.2 𝑚3
3600 𝑠
1ℎ
10 𝑚𝑚
1𝑚
3
= 72 km/h
= 7.2 x 109 𝑚𝑚3
Let’s do two as a class …
Problem 1:
100 mm3 → m3
100
Problem 2:
𝑚𝑚3
= 100
𝑚𝑚3
60 mi/h = ? m/s
𝑚𝑖
60
ℎ
=
𝑚𝑖 1.6 𝑘𝑚
60
ℎ
1 𝑚𝑖
3
1𝑚
103 𝑚𝑚
= 10-7 m3
HINT: 1 mi = 1609 m
103 𝑚
1 𝑘𝑚
1ℎ
3600 𝑠
= 27 m/s
Practice on your whiteboard …
hold it up when you are done
75
g/cm2
→
kg/m2
𝑔
75 2
𝑐𝑚
= 75
𝑔
1 𝑘𝑔
𝑐𝑚2 103 𝑔
102 cm
1m
2
= 750 kg/m2
Now practice more (use homework)..
If you are confident, do them by yourself.
If you are not confident, then work with someone who is confident.
BUT, the less confident one should be the one leading the practice
and talking out their process!!!!
Closure

What were our objectives today and how
did we meet them?

How did what we do today reflect our
statement of inquiry?

What was our learner profile trait, and
how did we demonstrate it?
Exit Ticket
1.
2.
3.
4.
0.05 cm = _______ mm
9.3 X 105 nm = __________ mm
3.5 m / s = __________ km / hr
35 m2 = __________ km2
Bonus: What is the difference between systematic and random
error?