Lecture 1

Dynamics of Rigid Bodies

MEC31

About the instructor

Conrad Allan Jay PantuaCredentials• BSME DLSU 2005• MSME NUS 2011

Email Class Site

[email protected] https://sites.google.com/site/mapuamec311/

Office

School of Mechanical Engineering

Textbook

Grading System

• 70% Long Quizzes (3-4 long quizzes)

• 20% Final exam

• 10% Seatwork and Homework

60% Passing Mark

Topics to be covered in this course

1. Kinematics of Particles

1.1 Rectilinear Motion with uniform acceleration

1.2 Rotational Motion

1.3 Rectangular Components of Curvilinear Motion of a particle

1.4 Flight of a projectile

1.5 General Rectilinear Motion

1.6 Normal and Tangential Components of Curvilinear motion of a particle

2. Kinetics of Particles

2.1 Newton’s laws of motion

2.2 Equation of Motion of a Particle

2.3 Units and dimensions

2.4 Effective force on a particle

2.5 Kinetics of Rectilinear translation-analysis as a particle

2.6 Particle kinetics applied to connected systems

Topics to be covered in this course

Engineering Mechanics

Rigid bodies

• A rigid body is any quantity of matter, the particles of which do not move relative to each other.

• The distance between any two points on the body will not change, regardless of the type of the force acting on the body.

• The condition of internal stress and distortion of bodies due to the action of forces is disregarded.

• That study (deformable bodies) is considered in Strength of materials.

What is Dynamics?

• Branch of mechanics that deals with the state of motion of particles and bodies under the action of forces.

• The study of this branch of mechanics in engineering must follow the study of statics, which deals with the effect of forces on bodies at rest or in a state of uniform motion.

Kinematics and Kinetics

Dynamics is subdivided into kinematics and kinetics.

Kinematics is the science which expresses the mathematical relationships existing between displacement, velocity, acceleration and time.

Kinetics is the study of the effect of unbalanced forces on the motion of bodies which therefore have accelerated or non-uniform motion.

Kinematics and Kinetics

Kinematics Kinetics

Motion of a particle

• If a particle is constrained to move along a straight line path, the motion is called rectilinear translation.

• If a particle is constrained to move along a curved path, the motion is known as curvilinear translation.

Rectilinear Translation

Curvilinear Translation

Rectilinear Motion with Uniform Acceleration

• Many of the problems usually encountered involve motion with uniform or constant acceleration.

• This type of motion arises when a body is acted upon by a resultant force which is constant.

Distance, Velocity and Acceleration

Distance or displacement (S) is a numerical description of how far apart objects are.

Distance, velocity, acceleration

t

sV Velocity is distance or displacement (s)

divided by time.

Acceleration is velocity (V) divided by time. t

Va

Formulas for Rectilinear Translation

2

22

2

1

2

attVs

asVV

atVV

o

O

O

Where:

V is the final velocity

Vo is the initial velocity

a is the acceleration (negative when decceleration)

s is the displacement

t is time