1. Dimensions, Units, and Error
CHAPTER 8
Dimensions, Units, and Error

2. Objectives Sections 8.1 Introduction 8.2 Dimensions and Units
Understand the difference between a unit and dimensions
Convert quantities between the different systems of measurement
Understand the types of error in a measurement
Express large numbers in scientific notation
Sections
8.1 Introduction
8.2 Dimensions and Units
8.3 Conversion between Different Units
8.4 Errors and Accuracy
8.5 Significant Digits
8.6 Summary

3. Basic Units and Dimensions
Unit is the basic quantity in a given system of measurement
yard, meter, inch
Some units can be a combination of different basic units
Example: Unit of force depends on the choice of the units of mass and acceleration
Dimension describes the quantity in terms of Mass, Length, Time and Temperature without specifying any unit.
Example:

4. Basic Units and Dimensions…2
One of the fundamental tenet for any physically valid equation is that dimensions on either side of the equation should be identical.
Now F=ma=kx. Now to get the units of stiffness k,
In fact dimensional analysis is used to check any proposed equation is valid or not.
Groups of quantities can be combined in a manner that the group becomes dimensionless and they oftentimes represent very important fundamental quantities.

5. 8.2 Systems and Measurement
There are three major systems of measurement
They are
BGS (British Gravitational System)
EES (English Engineering System)
SI System (The current worldwide standard)
BGS
Here force (not mass), feet (for length) and second (time) are the fundamental units.
Since, ,mass is derived unit.

6. Systems of Measurement…2
The unit of mass is a slug
Since weight is a force acting on mass of 1 slug
A body with a mass of 1 slug has a weight of lb.

7. Systems and Measurement…3
EES
Here the unit of mass is defined such that weight is 1 lbf
Mass is 1 lbm
For this system use SI
SI is the metric system. Fundamental units are grams (weight), cm ( length), and seconds (time).

8. Conversion between Units
We are faced with converting a quantity from one system to another. Use the logic that units should cancel on both sides
Example:
Conversion of
FPS SI
Force 1 lb = N
Mass 1 slug = kg
Length 1 ft = m

9. Comparison of Units in BGS, EES, and SI
Quantity
BGS EE SI
Mass
Slug
lbm
kilogram
Length ft
meter (m)
Time
sec (s)
Area
Velocity
Ft/s
M/s
Aceleration
Density
Force
Lbf
Newton(N)
Pressure
Pascal (Pa)
Energy
Ft x Lbf
Joule
Volume
Power
Ft x Lbf/s
Watt (W)

10. Order of 10 in metric system
Mult. Factor
Prefix
SI Symbol
tera T
giga G
mega M
kilo k
hecto h
deka da
deci d
centi c
milli m
micro
nano n
pico p
femto f
atto a

11. Errors and Accuracy Every quantity is measure in some form or another
Accuracy is defined as the difference between true value and measured value
All measurements contain error
Error has two parts
Bias error-inherent in the measurement systems. E.g. graduation in a tape
Precision error- Error that arises due to lack of repeatability. Arises due to operator or environmental conditions

12. Dimensions, Units, and Error
CHAPTER 8..concludes
Dimensions, Units, and Error