1-INTRODUCTION-TO-DYNAMICS.pdf

INTRODUCTION
TO DYNAMICS
CSPC-PSUB College of Engineering and Architecture
ENGR. ULYSSA MAE B. SERRANO
Class Instructor

1. Define the position, velocity, and acceleration of
a particle
2. Apply formulae in determining the change in
motion of particles
3. Define rectilinear motion
4. Explain the concept and type of rectilinear
motion
5. Apply the equations of rectilinear motion in
calculating the change in motion of a particle
LEARNING OBJECTIVE

The study of how rigid bodies react to forces
acting on them
Statics: The study of bodies
in equilibrium
Newton’s first law: FR =
0
Dynamics: The study of
motion
Kinematics – concerned
with the geometric aspects
of motion, s, v, a and t.

MOTION CONCEPT
𝒗 =
𝒔
𝒕
=
𝟏𝟎𝟎𝟎
𝟓
= 𝟐𝟎𝟎 𝒎/𝒔
1000 m
t=5 s

BASIC TERMINOLOGY
Position
Displacement
Distance
Velocity
Acceleration

DISPLACEMENT AND
DISTANCE
1 2 3

VELOCITY AND
ACCELERATION
1 2 3

ADDITIONAL TERMINOLOGY
Average Velocity – of the particle over the time
interval ∆t is defined as the quotient of the
displacement ∆x and the time interval ∆t:
Instantaneous Velocity, v – of the particle at the
instant t is obtained from the average velocity by
choosing shorter and shorter time intervals ∆t and
displacements ∆x:

ADDITIONAL TERMINOLOGY
Average Acceleration - of the particle over the time
interval ∆t is defined as the quotient of ∆v and ∆t:
Instantaneous acceleration, a – of the particle at the
instant t is obtained from the average acceleration
by choosing smaller and smaller values for ∆t and
∆v.

Kinematics – concerned with the geometric
aspects of motion: s, v, a, and t.
KINEMATICS
𝐯 =
𝐝𝐬
𝐝𝐭
𝐚 =
𝐝𝐯
𝐝𝐭
=
𝒅𝟐
𝒔
𝒅𝒕𝟐

Kinematics – concerned with the geometric
aspects of motion: s, v, a, and t.
KINEMATICS

The study of how rigid bodies react to forces
acting on them
Statics: The study of bodies
in equilibrium
Newton’s first law: FR
= 0
Dynamics: The study
of motion
Kinematics – concerned
with the geometric
aspects of motion, s, v, a
and t.
Kinetics – concerned
with how forces causing
the motion
Newton’s second law:
FR= ma

FORMULA
Note: only scalar equations are shown
from here on for simplification purpose

FORMULA
Principle of work and energy

FORMULA
Principle of linear impulse and momentum

Three common classes of motion:
1. 𝒂 = 𝒇(𝒕) Acceleration Is a Given Function of
time t
2. 𝒂 = 𝒇(𝒙) Acceleration Is a Given Function of
distance x
3. 𝒂 = 𝒇(𝒗) Acceleration Is a Given Function of
velocity v
DETERMINATION OF THE MOTION
OF A PARTICLE

Solving for dv and substituting f(t) for a, we write
Integrating
Specify the initial conditions of the motion
ACCELERATION IS A GIVEN
FUNCTION OF TIME, T

Specify the initial conditions of the motion
which yield v in terms of t
Solving for dx
FUNCTION OF TIME, T

Rearranging and substituting f(x) for a, we write
Since each member contains only one variable, we
can integrate the equation and obtain
FUNCTION OF DISTANCE, X

Since each member contains only one variable, we
can integrate the equation and obtain
which yields v in terms of x. We now solve for dt
FUNCTION OF DISTANCE, X

We substitute f(v) to obtain the following relations:
Integration of the first equation will yield a relation between v and
t; integration of the second equation will yield a relation between
v and x. Either of these relations can be used to obtain the
relation between x and t which characterizes the motion of the
particle.
FUNCTION OF VELOCITY, V

THANK YOU
CSPC-PSUB College of Engineering and Architecture
ENGR. ULYSSA MAE B. SERRANO
Class Instructor

1-INTRODUCTION-TO-DYNAMICS.pdf

More Related Content

Similar to 1-INTRODUCTION-TO-DYNAMICS.pdf

Recently uploaded

1-INTRODUCTION-TO-DYNAMICS.pdf