important lecture notes for dynamics

1. ENGINEERING MECHANICS
II
(DYNAMICS)

2. 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.

3. • 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.

4. • 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.

5. • The rapid technological developments of the present day requires
increasing application of the principles of mechanics, particularly
dynamics.

6. Area of application of dynamics
 Analysis and design of moving
structures.
 Fixed structure subjected to shock load.
 Robotic systems
 Automatic control system

7.  Rockets
 Missiles and spacecraft
 Transportation vehicle
 Machinery of all types, such as turbines, pumps, etc.

8. 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.

9. 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.

10. System of units
I. SI units
- Mass, time and length are taken as the basic units 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.

11. • The four fundamental quantities of mechanics
Quantity SI – units US – units
Mass Kg slug
Time s sec
Length m ft
Force N lb

12. • 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.

13. 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.

14. 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:
………………………………………..…………………………………………………..1.2
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.
2
2
1
r
m
m
G
=
F

15. • The acceleration due to gravity is derived from combining equation 1.1 and 1.2 ;
……………………………………1.3
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,
= 5.976x1024Kg
2
R
Gm
=
g e
e
m

16. Note: In almost all engineering problems where
measurements are made on the surface of the earth, the
effects of local vibration are neglected, and 9.81m/s2 in
SI unit is used for the sea level value of g.

17. • 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;
…………………………..1.4
R – radius of the earth
2
2
0
)
( h
R
R
g
=
g


18. 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.

19. 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 is 9.80665m/ or32.1740ft/
• 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.

45
2
s 2
sec

20. 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.

21. Example #2
(a)
(b)
(c)

22. Cont…
A space-shuttle payload module weighs 100 lb when resting on the
surface of the earth at a latitude of 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.

45

23. Cont…
• [For the surface-level value of the acceleration of gravity
relative to a rotating earth, use g=32.1740ft/
(9.80665m/ ) and,
• For the absolute value relative to a non-rotating earth, use
g= 32.234ft/ (9.825m/ )].
2
ec
s
2
ec
s
2
c
se
2
c
se

24. Ends
HERE!