Introduction to Dynamics
APPM 211
North-West University
Gabriel.Magalakwe@nwu.ac.za
9-14 February 2026
Lesson Outcomes
This introduction (overview) will cover the following:
(a) Importance of Statics,
(b) what kinematics of a particle entails (Chapter 12),
(c) what kinetics of a particle entails (Chapter 13),
(d) what work and energy principle entails (Chapter 14),
(e) what impulse and momentum principle entails (Chapter 15)
(f) what kinetics of a rigid body entails (Chapter 16)
What is Dynamics based on the above.
The importance of Statics
Fundamental Understanding of Forces and Equilibrium
Statics deals with analysing forces in systems at rest or in uniform
motion (zero acceleration).
Mastering this helps in understanding how forces interact, balance,
and maintain equilibrium.
This foundational knowledge is essential in dynamics, where
systems are no longer in equilibrium due to acceleration.
In summary, statics provides the critical groundwork for
understanding and mastering dynamics.
It equips students with the tools to analyse forces, develop
problem-solving strategies, and build the physical intuition needed
to tackle more complex, motion-based scenarios.
Kinematics of a particle
Kinematics of a particle refers to the study of a particle’s motion
without considering the forces causing movement, focusing on
aspects like position, velocity, and acceleration over time.
Kinetics analyses the forces acting on a particle and how they
influence object motion.
Basic Concepts:
Particle: An object with mass but negligible size, allowing its
motion to be described by a single point in space.
Reference Frame:
The coordinate system or viewpoint from which the motion is
observed, often Cartesian (x, y , z).
Kinematics of a particle
Types of Motion:
Rectilinear Motion: Motion along a straight line.
Curvilinear Motion: Motion along a curved path (e.g., projectile
motion, circular motion).
Position Vector (r): Describes the particle’s location in space.
dx
Velocity v = dr
dt Components: vx = dt ,
vy = dy
dt ,
vz = dz
dt .
Acceleration Components:
Tangential (at ) change in the speed along the path.
Normal or Centripetal (an ) change in the direction towards the
center (e.g., in circular motion).
Kinematics of a particle
Acceleration Components:
Radial (ar ) change in the speed along the radial direction.
Transversal (aθ ) change in the direction along the theta direction.
(e.g., in circular motion).
In polar coordinates: Radial (ar ) and transverse (aθ ) components
are components of the acceleration.
Relative Motion:
Relative Velocity: vA/B = vA − vB .
Describes the velocity of particle A relative to particle B.
Relative Acceleration: aA/B = aA − aB
Kinetics of a Particle
Kinetics of a particle is the branch of mechanics that focuses on
the relationship between the motion of a particle and the forces
causing that motion.
Unlike kinematics, which describes how particles move, kinetics
explains why they move by linking motion to external forces and
the particle’s mass. Hence why one needs to master the following:
Second Law : The net force acting on a particle equals the rate of
change of its momentum:
F = ma,
where F is the net force, m is the mass, and a is the acceleration.
Equations of Motion
Since
Fnet = ma
This vector equation can be resolved into components in different
coordinate systems:
Rectangular Coordinates:
P
Fx = max ,
P
Fy = may ,
P
Fz = maz .
Equations of Motion
When the motion is along a circular path, we consider the
following frame of reference:
Normal and tangential coordinates:
Useful for curved paths, where:
Ft = mat (tangential direction),
Fn = man (normal direction).
Transversal and radial coordinates
Useful for curved paths, where:
Fr = mar (radial direction),
Fθ = maθ (Transversal direction).
Work-Energy Principle
The work-energy principle relates the work done by forces to the
change in a particle’s kinetic energy:
X Z s2
1
1
Fds = mv22 − mv12 .
W =
2
2
s1
This principle is particularly useful when analyzing motion where
forces vary along the path. This solve a system that change
behaviour of distance when a force(s) acts on it to change velocity.
Conservation of Energy: In systems with no non-conservative
forces (like friction), the total mechanical energy (kinetic
+ potential) remains constant.
Principle of Impulse and Momentum
This principle relates (force applied over time) to the change in
momentum:
Z 2
F dt = mv2 − mv1 .
I=
1
Conservation of Momentum: In the absence of external forces,
the total momentum of a system remains constant.
Rotation About a Fixed Axis
Rotation about a fixed axis refers to the motion of a rigid body
where all points in the body move in circular paths around a single,
stationary axis. This axis can be vertical, horizontal, or inclined,
but it remains fixed in space.
Key kinematic quantities
Angular Displacement (θ): Measures the angle through which a
point or line has rotated around the axis, usually in radians.
Angular Velocity (ω): The rate of change of angular
displacement with respect to time:
ω=
dθ
.
dt
Rotation About a Fixed Axis
Angular Acceleration (α): The rate of change of angular
velocity with respect to time:
α=
dω
.
dt
Relationship between linear and angular quantities, for a point at a
distance r from the axis: Tangential velocity:
v = r ω.
Tangential acceleration:
at = r α.
Centripetal (radial) acceleration:
ar =
v2
= r ω2.
r
These concepts will be covered in detail, but it is important to
understand them in principle before doing the Dynamics.
Dankie vir julle aandag