Addis Ababa University
Addis Ababa Institute of Technology
School of Mechanical & Industrial Engineering
Engineering Mechanics II (Dynamics)
MEng 2052
Chapter One
Introduction
By Tadele Libay July, 2021
Introduction
• Dynamics is a branch of mechanics which deals with the
motion of bodies under the action of forces.
• The study of dynamics in engineering usually follows the
study of statics, which deals with the action of forces on
bodies at rest.
2
AAiT School of Mechanical and Industrial Engineering - SMiE
• Dynamics has two distinct parts:
i. Kinematics
ii. Kinetics
i. Kinematics- which is the study of motion without
reference to the forces which cause motion.
ii. Kinetics- which relates the action of forces on bodies to
their resulting motion.
3
AAiT School of Mechanical and Industrial Engineering - SMiE
• Dynamics is a relatively recent subject as compared with
statics.
• The understanding of dynamics was started about in 16th
centuries, and which is credited to Galileo.( showed that
heavy and light objects accelerated at the same constant
rate as they fall)
• Following Galileo, important contributions to mechanics
were made by, Newton's, Euler, D’Alembert, Lagrange,
Laplace, Einstein, ...and others.
4
AAiT School of Mechanical and Industrial Engineering - SMiE
Area of application of dynamics
The rapid technological developments of the present day requires
increasing application of the principles of mechanics, particularly
dynamics.
Analysis and design of moving structures.
Fixed structure subjected to shock load.
Robotic systems
Automatic control system
Rockets
Missiles and spacecraft
Transportation vehicle
Machinery of all types, such as turbines, pumps, etc.
5
AAiT School of Mechanical and Industrial Engineering - SMiE
6
AAiT School of Mechanical and Industrial Engineering - SMiE
Basic concepts and terms
Space – the geometric region occupied by bodies.
Time – is a measure of the succession of events and is considered an
absolute quantity in Newtonian mechanics.
Mass – is the quantitative measure of inertia or resistance to change
in motion of a body. Mass can also be defined as the quantity
of matter in a body or a property that gives rise to gravitational
attraction.
Force – vector action of one body on another.
7
AAiT School of Mechanical and Industrial Engineering - SMiE
Particle – a body of negligible dimensions.
- when the dimension of a body are irrelevant to the description
of its motion or the action of force on it, the body may be treated
as a particle.
Rigid body – is a body whose changes in shape are negligible
compared with the over all dimensions of the body or with the
changes in position of the body as a whole.
8
AAiT School of Mechanical and Industrial Engineering - SMiE
System of units
i. SI units
- Mass, time and length are taken as the basic quantities and the
units for force are derived from Newton’s 2nd law of motion.
ii. US customary units
- The unit for force, length and time are base units and the units
for mass are derived from the second law.
9
AAiT School of Mechanical and Industrial Engineering - SMiE
• The four fundamental quantities of mechanics
Quantity SI – units US – units
Mass Kg slug
Time s sec
Length m ft
Force N lb
10
AAiT School of Mechanical and Industrial Engineering - SMiE
• The SI system is termed an absolute system since mass is
taken to be an absolute or base quantity.
• The US customary system is termed a gravitational
system since force (as measured from gravitational pull)
is taken as a base quantity.
11
AAiT School of Mechanical and Industrial Engineering - SMiE
Newton's Laws of Motion
Law I – A particle remains at rest or continuous to move in a straight line
with a constant velocity if there is no unbalanced force acting on it.
Law II –The acceleration of a particle is proportional to the resultant force
acting on it and is in the direction of this force.
F = ma……………..……………………………..…….1.1
Law II –The force of action and reaction between interacting bodies are
equal in magnitude and opposite in direction and collinear.
12
AAiT School of Mechanical and Industrial Engineering - SMiE
Gravitation
• Newton states that two particles of masses m1 and m2 at a distance r from
each other attract each other with equal and opposite forces F and - F directed
along the line joining the particles is given by:
m1m2 ………………………………..…..………………………………………………….. 1.2
F=G
r2
Where:
F= the mutual force of attraction between two particles.
G= Universal constant = 6.673x10-11 m2/kg-s2
m1,m2 = the masses of the two particles
r = the distance between the centers of the particles.
13
AAiT School of Mechanical and Industrial Engineering - SMiE
• The acceleration due to gravity is derived from combining equation 1.1 and 1.2 ;
………………………………………..……1.3
Gme
g=
R2
Example 1: Determine the acceleration due to gravity at sea level(g) on a particle m.
Take: radius of earth, R=6,371km and mass of earth,
me = 5.976x1024Kg
14
AAiT School of Mechanical and Industrial Engineering - SMiE
Note: In almost all engineering problems where measurements are
made on the surface of the earth, the effects of local variations are
neglected, and 9.81m/s2 in SI unit is used for the sea level value of g.
15
AAiT School of Mechanical and Industrial Engineering - SMiE
• The variation of g with altitude is easily determined by the
gravitational law. If go represents the absolute acceleration due to
gravity at sea level, the absolute value at an altitude h is;
R2
g = g0
( R h) 2 …………………………………..1.4
R – radius of the earth
16
AAiT School of Mechanical and Industrial Engineering - SMiE
Effect of rotating earth
• The acceleration due to gravity as determined from the
gravitational law is the acceleration which would be measured
from a set of axes whose origin is at the center of the earth.
• With respect to this ‘fixed’ axes, this value may be termed the
absolute value of g.
• Because the earth rotates, the acceleration of a freely falling body
as measured from a position attached to the surface of the earth is
slightly less than the absolute value.
17
AAiT School of Mechanical and Industrial Engineering - SMiE
Standard value of g
• The standard value which has been adopted internationally for the
gravitational acceleration relative to the rotating earth at sea level
and at a latitude of 45 is 9.80665m/ s2 or 32.1740ft/sec2
• In almost all engineering applications near the surface of the earth,
we can neglect the difference between the absolute and relative
values of the gravitational acceleration, and the effect of local
variations.
18
AAiT School of Mechanical and Industrial Engineering - SMiE
Apparent weight
• If the gravitational force of attraction or true weight of the body is
W, then, because the body falls with an absolute acceleration g,
W = mg………………………………………..1.5
• The apparent weight is slightly less than the true weight of the
body.
• The difference is due to the rotation of the earth.
1
AAiT School of Mechanical and Industrial Engineering - SMiE 9
• [For the surface-level value of the acceleration of gravity
relative to a rotating earth, use g=32.1740 ft/sec2
(9.80665 m/s2) and,
• For the absolute value relative to a non-rotating earth, use
g= 32.234 ft/sec2 or (9.825 m/s2).
20
AAiT School of Mechanical and Industrial Engineering - SMiE
Example
A space-shuttle payload module weighs 100 lb when resting on the
surface of the earth at a latitude of 450 north.
a. Determine the mass of the module in both slugs and kilograms,
and its surface-level weight in Newton.
b. Now suppose the module is taken to an altitude of 200 miles
above the surface of the earth and released there with no velocity
relative to the center of the earth. Determine its weight under
these conditions in both pounds and newtons.
c. Finally, suppose the module is fixed inside the cargo bay of a
space shuttle. The shuttle is in a circular orbit at an altitude of 200
miles above the surface of the earth. Determine the weight of the
module in both pounds and newtons under these condition.
21
AAiT School of Mechanical and Industrial Engineering - SMiE
22
AAiT School of Mechanical and Industrial Engineering - SMiE
Suggested Problem
From 7th Edition , Merriam
Engineering Mechanics Dynamics
Chapter I Problem 1/……..
2, 5, and11
23
AAiT School of Mechanical and Industrial Engineering - SMiE
Thank You
Any Question?
24
AAiT School of Mechanical and Industrial Engineering - SMiE
