Engineering Mechanics –II (Dynamics)/2026
Chapter One
Introduction to Dynamics
1.1. Introduction
Mechanics is a branch of physical science that deals about the effect of force on bodies. It has
three broad categories;
 Rigid body mechanics
 Deformable body mechanics (about the strength of materials) and
 Fluid mechanics (about the mechanics of fluids)
The mechanics of rigid bodies is subdivided in to Statics and Dynamics.
Dynamics is a sub-branch of rigid body mechanics that deals about the motion of bodies
under the action of forces. In dynamics there are two distinct parts: kinematics and kinetics.
Kinematics deals with the motion of bodies without considering the force that causes the
motion. It is the study of the geometry of motion which is used to relate displacement,
velocity, acceleration, and time, without reference to the cause of the motion.
Kinetics deals with the motion of bodies in a relation to the force that causes the motion. It is
the study of the relation existing between the forces acting on a body, the mass of the body,
and the motion of the body. Kinetics is used to predict the motion caused by given forces or
to determine the forces required to produce a given motion.
1.2. Basic Concepts
Space: - The geometric region occupied by bodies is called space. Position in space is
determined relative to some geometric reference system by means of linear or angular
measurements.
Time: - Is a measure of the succession of events takes place.
Mass: - Is a quantitative measure of inertia of bodies. Mass may also be considered as the
quantity of matter in a body as well as the property which gives rise to gravitational
attraction.
Force: - Is the vector action of one body on another. It can be exerted by actual contact or at
a distance, as in the case of gravitational forces and magnetic forces. A force is characterized
by its point of application, its magnitude, and its direction.
Particle: - Is a body of negligible dimensions. When the dimensions 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. Example: - an Aeroplane flying in air & a car travelling from Jimma to Addis
Ababa.
Bililign F.
ECE
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Engineering Mechanics –II (Dynamics)/2026
Rigid body: - Is a body with considerable dimensions while analysing its motion. The study
of the mechanics of particles is a prerequisite to that of rigid bodies. Examples: a robot arm, a
car at a parking gate and movable machine parts.
1.3. Laws of Motion
The principles of dynamics are founded upon extensive experimental investigations. The first
note-worthy experiment was performed by Galileo (1564-1642). Other investigators followed
Galileo, among them being Newton (1642-1727), who, after carrying out a large number of
experiments, formulated the statements which are now known as Newton's Laws of Motion:
First law
In the absence of applied forces, a particle at rest remains at rest and a particle in motion
remains in motion, moving at a constant speed along a straight line.
Second Law
A particle subjected to an applied force will accelerate in the direction of the force, and the
acceleration will be proportional to the magnitude of the force and inversely proportional to
the mass of the particle. Analytically, this may be expressed as
F = ma
[1.1]
Where F-Force, m-mass & a-acceleration of a body
Third Law
To every action there is an equal and opposite reaction or the mutual actions of any two
bodies are always equal and oppositely directed. The two forces are always collinear.
1.4. Gravitation
Newton’s law of gravity states that:
The gravitational force (F) of attraction between two bodies, one of mass M and another of
mass m separated by a distance r, is proportional to (Mm)/r2 and lies along the line joining the
two centres. Analytically:
𝑀𝑚
F = G 𝑟2
[1.2]
Where G = universal constant called constant of gravitation which is about 6.673×10-11m3/(kg·s2)
Newton’s law of gravitation introduces the idea of an action exerted at a distance and extends
the range of application of Newton’s third law: the action F and the reaction -F in Fig. 1.1 are
equal and opposite, and they have the same line of action.
Bililign F.
ECE
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Engineering Mechanics –II (Dynamics)/2026
Fig 1.1
A particular case of great importance is that of the attraction of the earth on a particle located
on its surface. The force F exerted by the earth on the particle is then defined as the weight W
of the particle. Taking M equal to the mass of the earth, m equal to the mass of the particle,
and r equal to the radius R of the earth, and introducing the constant
𝑀𝑚
W = mg = G 𝑅2 Rearranging the equation:
𝐺𝑀
g = 𝑅2
[1.3]
Through experimental measurements: The mass M of the earth is 5.976×1024kg and the mean
radius R of the earth is 6.371×106m.
The value of g varies in a variation of both altitude and latitude. The variation of altitude
results in an increase of the distance between the two masses. This reduces the value of
acceleration due to gravity. Let go is the absolute value of gravity at the surface of the earth
and h is the altitude of the particle to the surface of the earth, then g at any altitude h is:
𝑅2
g = go (𝑅+ℎ)2
[1.4]
The standard value of g at sea level is 9.81m/s2(SI) or 32.174ft/s2 (US)
Bililign F.
ECE
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