Engineering Mechanics II
Dynamics
Bunyong Rungroungdouyboon
Faculty of Enginerring
Thammasat University
Chapter 1
Kinematics of Particles
1.1 Introduction
Dynamics
Kinematics
Kinetic
-Not related to force
- Related to force
Particles: Size doesn't matter
Only slide
Rigid Bodies: Size does matter
Slide + rotation
Chapter 1: Kinematics of Particles
1.2 Rectilinear Motion of Particles
1.7 Rectangular Component
1.8 Motion of Projectile
1.8 Motion of Projectile
- Only in x-y plane: vz and az = 0
1.9 Normal and Tangential Components
Unit Vectors
For convenience we define two new unit vectors.
=unit vector tangent to path
=unit vector normal to path
Note:
θ−ω−α
versus
s−v−a
Angular displacement, velocity, and acceleration are the rotational
analogies to linear s, v, and a.
They relate in very similar
ways to time:
[ rad ]
[ rad/s ]
[ rad/s2 ]
Circular Motion
An = v2/r = ω2 r
At = α•r
1.5 Cylindrical Coordinates (Polar Coordinates)
Transverse unit vector: eθ
Radial unit vector: er
Position of any particles can be defined as:
r = r er
Normal and Tangential Coordinate V.S. Polar Coordinates
1. r er : Constant
No Difference
Normal and Tangential Coordinate V.S. Polar Coordinates
2. r er : Not constant
Polar Coordinates are better
1.6 Dependent Motion of Two Particles
L= SA + CD + SB
VA = - V B
aA = - aB
1.7 Relative Motion for Two Particles
xB = xA + xB/A
VB = VA + VB/A
aB = aA + aB/A
Motion Summary
Rectangular Coordinate
Motion Summary
Normal and Tangential Coordinate
Motion Summary
Polar Coordinate
Summary
Summary