31
C H A P T E R 3
Dynamics of Particles
3.1 INTRODUCTION
Having studied kinematics of particles in the last chapter, dynamics of particles is introduced
in the present chapter. Briefly, dynamics is a branch of mechanics that deals with particles and
bodies in motion. Specifically, Newton’s laws of motion are presented in Section 3.2 while equa-
tions of motion and dynamic equilibrium of a particle are included in Section 3.3. Equations of
motion in radial and transverse components are presented in Section 3.4. Momentum and rate
of change of momentum of a particle are dealt with in Section 3.5. Angular momentum and rate
of change of angular momentum of a particle are studied in Section 3.6. Differential equation
for trajectory of a particle under a central force is included in Section 3.7.
3.2 NEWTON’S LAWS OF MOTION
Newton’s laws of motion governing the motion of a particle may generally be stated as in the
following three laws.
First Law: A particle continues in its state of rest or uniform motion in a straight line, unless
impressed forces act on it.
Second Law: A particle acts on by an impressed force (which is proportional to the time rate of
change of linear momentum of the particle) experiences an acceleration which has the same direction as
the force and a magnitude that is directly proportional to the force.
ird Law: Action and reaction in a particle are always equal and opposite.
Aside from the three laws stated in the foregoing, Newton’s law of gravitational attraction is stated
as follows.
Two given particles of matter attract each other with a force F proportional to their masses m
1
,
m
2
, and inversely proportional to the square of distance r between them. Mathematically,
F /
m
1
m
2
r
2
or F D G
m
1
m
2
r
2
; (3.1)
where G is called the universal constant of gravitation and has been experimentally determined
as G D 66:73 10
12
m
3
kg s
3
.
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