dimensions & unit conversions
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Dimensions & Unit Conversions
August 10 / 11, 2015
Dimensions & Units All physical quantities have dimensions and are
expressed in units. Dimension describes what the physical
quantity isUnits are how the quantity is measured
Example: SpeedSpeed has the dimensions of Length / TimeSpeed 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.
Distance, height,width
Length (L) meter (m)
Mass (m) Mass (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)
BasicPhysical Quantity
BasicSI Unit
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.
BasicDimension
DerivedPhysical Quantity
area L2 m2
Volume L3 m3
speed L/T m/s
acceleration L/T2 m/s2
forceML/T2 kg.m/s2
newton (N)
power M L2/T3 kg.m2/s3
watt (W)
densityM/ L3 kg/m3
DerivedDimension
Derived SI Unit
Go back to the measurements you did earlier & fill in the rest of the table
Quantity measured
Measurement
Dimensions
Units SI or not?
Smaller units
every step is 10± 1 powerThey are grouped into steps 10± 3
femto pico nano micro mili kilo mega giga tera f p n m m k M G T
base unit1
Larger units
10-15 10-12 10-9 10-6 10-3 100 103 106 109 1012
centi deci c d 10-2 10-1
f p n m m k M G T1
10-15 10-12 10-9 10-6 10-3 100 103 106 109 1012
5𝑚ℓ=¿ℓ
larger unit →smaller number
c d 10-2 10-1
The problem: We have to convert 5 into kl. Will the number in front of kl be smaller or bigger? Smaller!!
SI conversions!
SI conversions!
f p n m m k M G T1
10-15 10-12 10-9 10-6 10-3 100 103 106 109 1012
5𝑚ℓ=¿ℓ
larger unit →smaller number
5𝑚ℓ=5𝑚 ℓ×( 1𝑘ℓ106𝑚ℓ )=5×10
− 6𝑘 ℓ
= 1
5𝑚ℓ={6 𝑠𝑡𝑒𝑝𝑠𝑡𝑜 h𝑡 𝑒 h𝑟𝑖𝑔 𝑡0.000005 }=5×10− 6𝑘ℓ
c d 10-2 10-1
* Note: The larger unit always has a 1 in the conversion factor (i.e. 1 kℓ and 1 km).
We can do SI unit conversions in two different methods:
Method 1: Conversion factors
Method 2: Moving the decimal
Moving the decimal seems so much easier … why do we bother with conversion factors?
Because sometimes moving the decimal won’t work … more on this later!
f p n m m k M G T1
10-15 10-12 10-9 10-6 10-3 100 103 106 109 1012
5𝑘𝑚=¿¿
smaller unit →bigger number
5𝑘𝑚=5𝑘𝑚×( 105𝑐𝑚1𝑘𝑚 )=5×105𝑐𝑚
= 1
c d 10-2 10-1
5𝑘𝑚={5 𝑠𝑡𝑒𝑝𝑠𝑡𝑜 h𝑡 𝑒 𝑙𝑒𝑓𝑡500000 𝑐𝑚 }=5×105𝑐𝑚
Another problem!Will the number in front of cm be smaller or bigger? larger!!
Method 1: Conversion factors
Method 2: Moving the decimals
The wavelength of green light is 500 nm. How many meters is this?
500𝑛𝑚×( 1𝑚109𝑛𝑚 )=500×10
− 9𝑚=5×10− 7𝑚
or
500𝑛𝑚=0.0000005𝑚=5×10−7𝑚
One more as a class …
I have 906 gigabyte hard drive on my computer. How many bytes of data will it hold?
Practice using both methods on your whiteboard … hold it up when you are done
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. How many liters is 16 ℓ ?
2. 4.3 x 104 ns = ? µs
3. 5.2 x 108 ms = ? ks
4. 0.09 cm = ? pm
16𝜇 ℓ=1.6×10−5 ℓ
4.3 = 43 µs
5.2×108𝑚𝑠=520𝑘𝑠8 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
Example 2: 7.2 m3 → mm3
20 = 20 = 72 km/h
= 7.2 x
Let’s do two as a class …
Problem 1:
Problem 2:
100 mm3 → m3
= 10-7 m3
60 mi/h = ? m/s HINT: 1 mi = 1609 m
60 = 27 m/s
Practice on your whiteboard … hold it up when you are done
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!!!!
75 g/cm2 → kg/m2 75 = 750 kg/m2
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. 0.05 cm = _______ mm2. 9.3 X 105 nm = __________ mm3. 3.5 m / s = __________ km / hr4. 35 m2 = __________ km2
Bonus: What is the difference between systematic and random
error?
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