1. Statics
Statics is concerned with the equilibrium of bodies that are at rest or moving with a constant velocity
Dynamics is concerned with bodies that are undergoing acceleration

2. Basic quantities used throughout mechanics
Length
locates the position of a point in space
able to describe the size of a physical system
Time
succession of events
statics problems are time independent
Mass
property of matter
provides quantitative measure of the resistance of matter to a change in velocity
Force
“push” or “pull” exerted by one body on another
characterized by magnitude, direction, sense, and point of application

3. Idealizations Particle Rigid body Concentrated force
has mass, but a size that can be neglected
geometry of the body not involved in the analysis
Rigid body
can be considered a combination of a large number particles
particles remain at the same fixed distance from one another both before and after applying a load
Concentrated force
a loading which is assumed to act at a point on a body

4. Units of measure
International System of Units (modern version of the metric system) - SI
US Customary System of Units – FPS
W = m g
(g is the acceleration due to gravity, 9.81 m/s2 or 32.2 ft/s2)
Angular units may be expressed in radians
quantity SI
FPS
length
meter (m)
foot (ft)
time
second (s)
mass
kilogram (kg)
slug ((lb-s2)/ft)
force
Newton (N, (kg-m)/s2)
pound (lb)

5. SI unit prefixes multiple/ submultiple exponential form prefix
SI symbol
109
giga G
106
mega M
1 000
103
kilo k
0.001
10-3
milli m
10-6
micro μ
10-9
nano n

6. Rules for use of units/symbols and prefixes
Never written with a plural “s”
Always written in lowercase letters, except M, G, and units named after a person (i.e. Newton, N)
Quantities defined by several units which are multiples of one another are separated by a dot (a dash will be used in these slides, i.e. m-s represents meter-seconds, while ms represents milliseconds)
μN2 = (μN)2 = μN * μN
When performing calculations, begin by representing numbers in terms of base units and/or derived units
(50 kN)(60 nm) = (50)(103)(N) * (60)(10-9)(m) =
3 000 (10-6) N-m = 3 (103)(10-6) N-m = 3 N-mm
Compound prefixes should not by used (kμs)
Avoid use of prefix in denominator of composed units, except kg

7. Significant figures
Accuracy of a number is specified by the number of significant figures it contains
A significant figure is any digit, including a zero, provided it is not used to specify the location of the decimal point for the number
763,000 ??? if only four significant digits
Use scientific notation, x 105, one digit to the left of decimal point with the remaining digits to the right
Use engineering notation, x 106 – the exponent is displayed in multiples of three (to facilitate conversion of units to those having an appropriate prefix)

8. Rounding
If the n + 1 digit is less than 5, the n + 1 digit and others following it are dropped
If the n + 1 digit is greater than 5 (or is equal to 5 with nonzero numbers following the 5), then increase the nth digit by 1 and drop the n + 1 digit and others following it
If the n + 1 digit is equal to 5 (with no numbers or zeroes following the 5)
And the nth digit is an even number, then the nth digit is not rounded up
And the nth digit is an odd number, then the nth digit is rounded up
In text, the answers to problems are generally rounded to three significant figures

9. General procedure for analysis
Read the problem carefully and try to correlate the actual physical situation with the theory studied.
Draw any necessary diagrams and tabulate the problem data.
Apply the relevant principles, generally in mathematical form.
Solve the necessary equations algebraically as far as practical, then making sure they are dimensionally homogeneous, use a consistent set of units and complete the solution numerically. Report the answer with no more significant figures than the accuracy of the given data (generally three significant figures for problems in this text).
Study the answer with technical judgment and common sense to determine whether or not it seems reasonable.