Lecture 4
1.3.2. Circular Motion
(2) Velocity in circular motion
(3) Acceleration in circular motion
Circular Motion
D
D
, I , I
d
=
dt
d = dt
d
=
dt
d = dt
d = d
(2) Velocity of a particle
in circular motion
y
v
= dr
v
dt
r = r0 er
r0
O
er = cos i + s
Lecture 5
1.4 Planar Curvilinear Motion
of Particles
in Cartesian coordinate System
in Path Coordinate System
Motion of a Particle
Rectilinear motion
Simple
Circular motion
Combination
General
Curvilinear
motion
Curvilinear
motion
Rectilinear motion + Rec
Lecture 7
1.5 Motion of a particle
Relative to
a Point Attached
translating frame
Given motions of A and B
z
Absolute path of B
BB
BB
rBA is a function of time
O
x
AA
A
A
y
Absolute path of A
Attached a translating ref. to A
z
B
z
O
x
x
A
y
y
What is the
Lecture 8
1.6 Constrained Motion of
Connected Particles
A particle moving freely in 3-D space
z
A (xA, yA, zA)
k
i
x
O
j
three
y Independent
coordinates
For a particle P in motion
degree of freedom (d.o.f.)
is defined to be
the Number
of Independent coord
Lecture 9
2.1 Introduction to
Planar Kinematics of rigid bodies
2.2 Simple planar motion
of a rigid body
2.3 General planar motion
2.3.1. Combination of Translation
and Rotation
2.1 Introduction to Planar Kinematics
of rigid body
z All points of the body
Lecture 10
2.3 General plane motion
2.3.1 Combination of Translation &
Rotation
Typical general planar motion
- A wheel rolls without slipping
2.3.2 Instantaneous center of velocity
Example 2-3
Typical general planar motion
- A wheel rolls without slippin
Lecture 11
2.4 Motion Relative to
a Body Attached Reference
A body relative to another body
A point/particle relative to a body
2.4.1 Principle of angular Vel./Ac Combination
Relative and Entrained rotation
2.4.2 Principle of Velocity Combination
Relative
Lecture 12
2.4 Motion Relative to
a Body Attached Reference
2.4.3. Principle of Accel. Combination
Relative acceleration
Entrained acceleration
Coriolis acceleration
Angular acceleration of
A body relative to another body
2
2
2
1
1
2 - 1
1
1
2
= 1
=
2
A
MA1001
DYNAMICS
Kinematics
Particles
Rigid bodies
Kinetics
Particles
Rigid bodies
What is kinetics ?
Causes of motion
Forces & inertia are involved
inertia are involved
Given forces motion ?
Given motion forces ?
Given forces & motion inertia ?
What are
Thi
This Lecture covers
3.1. Newtons law (F=ma)
Newton law (F=ma)
(continued)
(continued)
3.2. Alternative form of Newtons second law
- Principle of Angular Momentum
F ma
F : N Resultant Force
m:
kg, measure of inertia
2
ma : kg m/s , Rate of change of
:
Concepts
Linear
Angular
Inertia
m
Io
Velocity
v
L mv
H o I o
Acceleration
a
Force
F
Mo r F
Momentum
Principle
F ma
M
o
I o
Motion on a horizontal plane = Ignore gravity
Kinetics of Curvilinear Motion
Kinetics of Curvilinear Motion
A new application
Micr
Three state functions of motion
Linear momentum
L mv
Angular momentum
H A rPA L
Kinetic energy
energy
12
T mv
2
This lecture covers
3.4. Principle of Linear/Angular
Impulse and Momentum
Impulse
Impulse = Momentum
Linear impulse, I12
impulse
t2
F d L2
This lecture covers
This lecture covers
3.5. Conservative Force and Potential Energy
Conservative Force and Potential Energy
- Conservation of Total Energy
3.5.1. Gravitational force
3.5.2. Linear Spring Elastic Force
Sp
3.5.3. Conservative Systems
with I
This lecture covers
This lecture covers
3.6. Conservation of
Linear/Angular Momentum
3.6.1 Conservation of Linear Momentum
Conservation:
Unchanged
During the History of motion
the History of motion
Fully conserved:
Partly conserved:
L constant
mv x const.
This lecture covers
This lecture covers
3.7. Collision and Impact Force
3.7.1. Direct Central Collision
3.7.2. Oblique Central Collision
3.7.1. Direct Central Collision
z
B
vB
vA
A
y
O
x
Action line of impact forces
v B0
FAB
v A0
B
A
FBA
e
v B1 ?
v A1 ?
L
G163
DYNAMICS
Kinematics
Particles
Rigid bodies
Kinetics
Particles
Rigid bodies
Kinetics of
particles
ti
Kinetics of rigid
bodies
Newtons
Second Law
Principle of
Linear
Impulse & momentum
Principle of
Angular
Impulse & momentum
Principle of
Work and Energ
MA1001 DYNAMICS
Lecturer :
Office :
Phone :
E-mail :
A/P YAP Fook Fah
N3.2 - 02 - 15
6790 4724
[email protected]
MA1001 Learning Outcome
Upon successful completion of the course, students will be able to:
a) Analyze the kinematics of a particle in order t
Lecture 2
1.2. Position, velocity and
acceleration
1.2.1. Displacement vector,
and Relative position vector
1.2.2. Velocity
1.2.3. Acceleration
1.2.1. Displacement vector,
and Relative position vector
z
P1 (x1 , y1 , z1 )
rP1
O
x
rP 2
P2 (x2 , y2 z2 )
y
r
Lecture 3
1.3. Simple Plane Motion of a Particle
1.3.1. Rectilinear Motion
1.3.2. Circular Motion
Motion of a Particle
Rectilinear motion
Simple
Circular motion
Combination
General
Curvilinear
motion
1.3.1. Rectilinear Motion
Position vector
O
P
r = x i
x