1. Units, Standards, SI System

2. Units, Standards, SI System
All measured physical quantities have units.
Units are VITAL in physics!!
In this course (& in most of the modern world, except the USA!) we’ll use (almost) exclusively the SI system of units.
SI = “Systéme International”
(French)
More commonly called the “MKS system” (Meter-Kilogram-Second) or more simply,
“The Metric System”

3. Meter (m) (kilometer = km = 1,000 m)
SI or MKS System
Standards for
Length, Mass, & Time
Length Unit:
Meter (m) (kilometer = km = 1,000 m)
Standard Meter: Modern definition in terms of the speed of light (c = 3  108 m/s)
1 meter  Length of path traveled by light in vacuum in [1/(3  108)]* of a second!
*(more precisely, [1/299,792,458]!)

4. Definition of the Meter
The original definition of a meter was in
terms of the Earth’s circumference.
It was then changed to be based on this platinum-iridium bar (figure).
It is now defined in terms of the
speed of light, as already
mentioned.

5. SI or MKS System Standards for Length, Mass, & Time Time Unit:
Second (s)
Standard Second: Modern definition in terms of nuclear decay:
1 Second  Time required for
[9.19  109]* oscillations of radiation emitted by cesium atoms!
*(more precisely, [9,192,631,770]!)

6. Standards & Technology.
Definition of a Second
The value of the second is based on the frequency of
light emitted by cesium atoms.
Shown in the figure is a cesium clock in the
National Institute of
Standards & Technology.

7. SI or MKS System
Standards for
Length, Mass, & Time
Mass Unit:
Kilogram (kg)
Standard Kilogram  Mass of a specific platinum-iridium alloy cylinder kept at the International Bureau of Weights & Measures in France. (Discussed more later)

8. Larger & Smaller units are defined from the SI standards by using powers of 10 & Greek prefixes.
The table gives the
standard SI prefixes for indicating powers of 10.
Many (k, c, m, μ) are familiar; Y, Z, E, h, da, a, z, & y are rarely used. __  __  __  __ 

9. Typical Lengths (approximate)
  


10. Typical Lengths (approximate)            
TABLE 1.1 *Red blood cells are not spherical, but are shaped more like flat plates. The value given here is the approximate diameter of the plate.

11. Typical Times (approximate)             

12. Typical Times (approximate)    
TABLE 1.2     

13. Definition of a Kilogram
Mass is related to the amount of material contained in an object.
All masses are defined in terms of a Standard Kilogram, which is composed of an alloy
of platinum & iridium.

14. Typical Masses (approximate)         

15. Typical Masses (approximate) 
TABLE 1.3        

16. only in the SI system, kilograms, meters, & seconds.
Other Systems of Units
We will work
only in the SI system,
in which the base units are
kilograms, meters,
& seconds.

17. 1. The CGS or “Lesser Metric System” Base Quantities are defined in
Other Systems of Units
1. The CGS or “Lesser Metric System”
Base Quantities are defined in
terms of The SI Base Quantities:
Mass Unit = gram (g)  10-3 kg
Length Unit = centimeter (cm)  10-2 m
Time Unit = second (s)
(unchanged from the SI system)

18. The Engineering System & We will work exclusively in the SI System!
Other Systems of Units
2. The British System: Also known as
The Engineering System &
The (US) Customary System
Base Quantities: Foot, Pound, Second (fps)
In this system, Force in Pounds is a base unit,
instead of mass as used in the SI system.
Obviously, there are conversion factors to convert between the
British & the SI Systems. These are well known & can be looked
up if they are needed.
Unit Conversions like this are NOT physics & we will
NOT be doing them!
We will work exclusively in the SI System!

19. Fundamental Quantities & Their Units
Quantity
SI Unit
Length
meter
Mass
kilogram
Time
second
Temperature
Kelvin
Electric Current
Ampere
Luminous Intensity
Candela
Amount of Substance
mole
Physics I,
Phys 1403
Physics II,
Phys 1404

20. Units Summary

21. In this class, we will NOT do unit conversions!
We will work exclusively in SI (MKS) units!

22. Basic & Derived Quantities
Basic Quantity  Must be defined in terms of a standard:
Meter, Kilogram, Second.
Derived Quantity  Defined in terms of combinations of basic quantities
Unit of speed (v = distance/time)
= meter/second = m/s
Unit of density (ρ = m/V) = kg/m3

23. t = (⅔)hr so, x = (90 km/hr)  [(⅔)hr] = 60 km
Units and Equations
In dealing with equations, remember that the units must be the same on both sides of an equation (otherwise, it is not an equation)!
Example: You go 90 km/hr for 40 minutes.
How far did you go?
A Ch. 2 equation: x = vt. v = 90 km/hr, t = 40 min.
To use this equation, first convert t to hours:
t = (⅔)hr so, x = (90 km/hr)  [(⅔)hr] = 60 km
The hour unit (hr) has (literally!) cancelled out in the numerator & denominator!

24. 1 m/s  3.6 km/hr; 1 km/hr  (1/3.6) m/s
Converting Units
As in the example, units in the numerator & the denominator can cancel out (as in algebra)
Illustration: Convert 80 km/hr to m/s
Conversions: 1 km = 1000 m; 1hr = 3600 s
 80 km/hr =
(80 km/hr) (1000 m/km) (1hr/3600 s)
(Cancel units!)
80 km/hr  22 m/s
(22.222…m/s)
Some useful conversions:
1 m/s  3.6 km/hr; 1 km/hr  (1/3.6) m/s

25. Order of Magnitude & Rapid Estimating: “Fermi Problems”
Sometimes, we are interested in only an approximate value for a quantity.
We are interested in obtaining rough or
Order of Magnitude Estimates.
Order of Magnitude Estimates are made by rounding off all numbers in a calculation to 1 sig fig, along with power of 10.
Can be accurate to within a factor of 10 (often better)
Sometimes these are called
“Fermi Problems”.

26. Example: V = πr2d Example: Estimate!
Estimate the volume of the water in a particular lake, which is roughly circular, about 1 km across, & you guess it has an average depth of about 10 m.
Example: Estimate!

27. Example: Thickness of a Page You don’t need one of these!
Estimate the thickness of a page of your textbook.
Hint:
You don’t need one of these!
Figure 1-8. Caption: Example 1–6. Micrometer used for measuring small thicknesses.
Answer: Measure the thickness of 100 pages. You should find that the thickness of a single page is about 6 x 10-2 mm.

28. Example: Height by Triangulation. Estimate the height of
the building shown by “triangulation,” with
the help of a bus-stop
pole and a friend. (See how useful the diagram is!)
Figure 1-9. Caption: Example 1–7. Diagrams are really useful!
Answer: The building is about 15 m tall.

29. Dimensions & Dimensional Analysis
The dimensions of a quantity are the base
units that make it up.
Generally they are written using square brackets.
Example: Speed = distance/time
Dimensions of Speed: [L/T]
Quantities that are being added or subtracted
must have the same dimensions. In addition,
a quantity calculated as the solution to a
problem should have the correct dimensions.

30.  The correct units can easily be found! ρ = m/V Density unit = kg/m3
Dimensional Analysis
If the formula for a physical quantity is known
 The correct units can easily be found!
Example: Volume:
V = L3  Volume unit = m3
A cube with L =1 mm
 V = 1 mm3 = 10-9 m3
Example: Density:
ρ = m/V Density unit = kg/m3
ρ = 5.3 kg/m3 = g/mm3

31.  The correct formula can be “guessed”! Acceleration unit = m/s2
Dimensional Analysis
If the units of a physical quantity are known
 The correct formula can be “guessed”!
Examples:
Velocity: A car’s velocity is 60 km/h
Velocity unit = km/h
 Formula: v = d/t
(d = distance, t = time)
Acceleration: A car’s acceleration is 5 m/s2
Acceleration unit = m/s2
 Formula: a = v/t
(v = velocity, t = time)

32. Example: Is this the correct equation for velocity?
Dimensional Analysis = Checking dimensions
of all quantities in an equation to ensure that
those which are added, subtracted, or equated
have the same dimensions.
Example: Is this the correct equation for velocity?

33. Example: Is this the correct equation for velocity?
Dimensional Analysis = Checking dimensions
of all quantities in an equation to ensure that
those which are added, subtracted, or equated
have the same dimensions.
Example: Is this the correct equation for velocity?
Check the dimensions:

34. Example: Is this the correct equation for velocity?
Dimensional Analysis = Checking dimensions
of all quantities in an equation to ensure that
those which are added, subtracted, or equated
have the same dimensions.
Example: Is this the correct equation for velocity?
Check the dimensions:
Wrong!

35. Dimensional Analysis