BES 2 - Dynamics of Rigid Bodies
Introduction to
Dynamics
Prepare by: Sir Kristian Nino J. Ignacio
Petroleum Engineering Department
2023
Learning Outcomes
• Define the concepts of position, displacement, velocity and
acceleration.
• Calculate the particle motion along a straight line and represent
this motion graphically.
• Define kinetics and kinematics of a particle.
Why study dynamics?
• As a subject of study, it is
crucial for understanding
systems made up of a single
body or several bodies
interacting with one another.
• Predicting an object or
objects' motion under the
influence of various forces,
such as gravity or a spring,
requires a dynamics analysis.
PRINCIPLES OF DYNAMICS
• DYNAMICS – is the branch of mechanics which deals with the
study of bodies in motion.
• PARTICLE – an object of point size. A body so small that any
differences in motions of its parts can be neglected.
• Body – a system of particles which form an object of
appreciable size.
KINEMATICS AND KINETICS
• KINEMATICS – is the branch of
•
•
•
•
mechanics concerned with the
geometric aspects of motion.
used to define the motion of a
particle or body without
consideration of the forces causing
the motion.
A treatment of the relations
between:
Displacement (where is the
particle)(position in space)
velocity (how fast is the particle
travelling)
• acceleration
KINEMATICS AND KINETICS
• KINETICS – the branch of mechanics that relates the force
acting on a body to its mass and acceleration.
MOTION OF A PARTICLE
•
•
Position - location of the particle at any given instant.
Displacement – is the vector distance from an origin to the
position occupied by the particle on its path of travel.
MOTION OF A PARTICLE
• Velocity – the time rate of change of position.
• Average Velocity
• Instantaneous Velocity
MOTION OF A PARTICLE
•
•
Acceleration – time rate of
change of velocity.
Basically, a time rate of
change, of a time rate of
change.
MOTION OF A PARTICLE
• Three important kinematic relations
CONSTANT ACCELERATION
• VELOCITY AS A FUNCTION OF TIME
CONSTANT ACCELERATION
• POSITION AS A FUNCTION OF TIME
CONSTANT ACCELERATION
• VELOCITY AS A FUNCTION OF POSITION
IMPORTANT EQUATIONS AT CONSTANT
ACCELERATION
Important Points
•
•
•
•
•
•
Dynamics is concerned with bodies that have accelerated motion.
Kinematics is a study of the geometry of the motion.
Kinetics is a study of the forces that cause the motion.
Rectilinear kinematics refers to straight-line motion.
Speed refers to the magnitude of velocity.
Average speed is the total distance traveled divided by the total time. This
is different from the average velocity, which is the displacement divided by
the time.
• A particle that is slowing down is decelerating.
• A particle can have an acceleration and yet have zero velocity.
EXAMPLE 1
• During a test a rocket travels
upward at 75 m/s, and when it is
40 m from the ground its engine
fails. Determine the maximum
height sB reached by the rocket
and its speed just before it hits the
ground. While in motion the rocket
is subjected to a constant
downward acceleration of 9.81
m/s2 due to gravity. Neglect the
effect of air resistance.
EXAMPLE 2
• A particle travels along a straight line with a velocity of 𝑣 = (4𝑡 − 3𝑡 2 )𝑚/𝑠,
where t is in seconds. Determine the position of the particle when 𝑡 =
4𝑠. 𝑠 = 0 𝑤ℎ𝑒𝑛 𝑡 = 0.
ACTIVITY 1 (SEATWORK)
• A car starts from rest and with constant acceleration achieves a
velocity of 15 m/s when it travels a distance of 200 m.
Determine the acceleration of the car and the time required.
• A train starts from rest at a station and travels with a constant
acceleration of 1 m/s2. Determine the velocity of the train when
t = 30 s and the distance traveled during this time.