DYNAMICS

Dynamics is that part of engineering mechanics in which a study is made of particles and bodies in motion; it is divided into branches-namely, kinematics and kinetics. Kinematics consists essentially of deriving equations relating to displacement, velocity, acceleration and time. Kinetics consists essentially of deriving equations relating to the unbalanced force or the unbalanced moment to the change in motion.

Kinematics:

Types of particle motion -

1. Rectilinear motion

   
   

2. Curvilinear motion

   

Types of Rigid Body Plane Motion:

1. Rectilinear Translation - all particles move on parallel straight lines and have same displacements, velocities and accelerations.

2. Curvilinear Translation - same as above except that all particles move on congruent curves.

3. Fixed Axis Rotation - all particles move on concentric circular paths

   
   

   For Particle P -

   Tangential acceleration of particle

   Normal acceleration of particle

4. General Plane Motion - a motion which can be resolved into translation plus fixed axis rotation

   
   

Kinetics:

Newton's 2nd Law of Motion for a particle-

• F = unbalanced force

• m = mass of particles

• a = absolute acceleration

For English Gravitation System of Units-

For a system of particles (rigid or non-rigid body)-

• F = unbalanced force

• M = mass of system of particles

• a = absolute acceleration of center of mass

For rigid-body rotation about fixed axis

(M _o) _z = (I _o) _z ^?

where ?(M _o) _z is unbalanced moment about axis of rotation

Work Energy Principle

By taking Newton's 2nd Law of Motion and using components...