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?