PARTICLE KINETICS: WORK AND ENERGY

In physics, we define work as force with a certain displacement. However, the displacement would need to be conforming to the motion of the object. This condition makes the definition tricky. 

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On the other, energy derived its definition from work. (Energy is the ability to work. From the meaning of these two quantities, it is easy to sort that they are interchanging parameters. There are a number of kinds of energy discussed in Dynamics. The Law on Conservation of Energy is also used to lead the understanding to Work-Energy Principle. WEP is another method in solving the parameters required in kinematics - instead of the basic motion formulas to be used, the method uses the correlation between work and energy.

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PARTICLE KINETICS: FORCE, MASS AND ACCELERATION

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After kinematics, the other part of Dynamics is kinetics which deals with the force responsible for motion in the analysis of bodies. Kinetics will be relating force to acceleration, velocity, distance traveled and time.

Particle kinetics have been subdivided into three important parts:

1. Force, mass, and acceleration
2. Work-energy
3. Impulse and momentum

Special applications for kinetics deal with
a. Impact
b. Central-force motion
c. Relative motion

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PARTICLE KINEMATICS: DEPENDENT MOTION

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In contrary to the principle with relative motion where two or more particles are moving independently, dependent motion has one particle's movement depending on the other. This motion commonly occur between interconnected particles with cords and pulley systems.

There are various pulley systems that can be considered in this case. 

1. A single rope system where one cord goes around pulleys and the particles under study.
2. Two and more rope systems where there can be 2 or more ropes involved in the system.

No matter which system is involved, the analysis would be easier by using CSLM (constant string length method). Analysis on the velocity and acceleration of the particles would have to start with the position or the length. Later on, after identifying which equation to use, time derivatives are used to transform the length equation to either velocity or acceleration equation.


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PARTICLE KINEMATICS: TRANSLATING AXES

Previous discussions in the study of the motion of particles used a fixed reference usually denoted as the x-y-z axes or the i-j-k planes. Translating axes is one way to determine the relative motion of a particle with respect to another. This is like identifying the position, velocity or acceleration of a particle from the point of view of another moving particle.

Usual examples are cars meeting at an intersection, a speedboat going against the current, two airplanes flying and so on.

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PARTICLE KINEMATICS: CURVILINEAR MOTION

The motion of a particle has been described to move in two ways: planar or rectilinear and curvilinear. From the name itself, curvilinear motion is described as the curved path of a particle in motion. There are two ways in which this motion is further categorized:

1. Plane  curvilinear motion where the coordinates of the motion is taken like of a cylinder. Plane curvilinear motion is best described as a 2-D analysis of a particle moving in a curved path. 

2. Space curvilinear motion is the 3-D counterpart of the previous motion whereby the path is described as directed to an osculating plane.

Curvilinear motion will be further discussed by the three different coordinate system used to analyze it.


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a. Rectangular coordinates - using the -x and -y components of the path
b. Normal and Tangential components - using the parallel and the perpendicular components of the path
c. Polar coodinates (Cylindrical coordinates) which is best used when motion is restricted to the plane.

KINEMATICS: RECTILINEAR MOTION

Rectilinear motion in kinematics studies an object moving in a straight line. Although the motion is defined as straight, this is further categorized as continuous motion and erratic motion.

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Continuous motion has a defined way of moving in terms of position, velocity and acceleration, whereas, erratic motion has changing motion whereby its position, velocity and acceleration are hard to describe using one continuous mathematical equation in the path. This motion would have to be dissected and studied by segments.

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Continuous motion is the primary course in Physics, however, in Dynamics, students would much more understand how the basic equations applied to this subject have been derived through Calculus. Furthermore, examples would be applying differentiation and integration - more advanced functions from Physics.

Erratic motion deals more on graphs to help visualize the motion of the body. The s-t, v-t, and a-t graphs are used to identify the parameters for this kind of motion. And with the rich variance of how graphs would appear, erratic motion computation would usually be imploring segments which are later added together to arrive at a certain answer.

BASIC CONCEPTS OF DYNAMICS

Mechanics is defined as that branch of physical science which focuses on the study of the states of a body acted upon by forces. The states are for equilibrium or at rest and in motion. This definition further discusses the difference of studies taken with the different kinds of bodies. As those observed, bodies are categorized as rigid bodies, those which are studied as they are, and deformable bodies, those bodies which change shape as forces are applied on them.

The study of the state of rigid bodies are further classified under Statics, which deals with rigid bodies in equilibrium or at rest and Dynamics, the study of rigid bodies in motion. Moreover, the study of deformable bodies is known as Strength of Materials.

For our discussion, we will be focused more on rigid bodies in motion - Dynamics!

Dynamics as a course is just the extension of Physics, motion and forces. The two general types summarizing this course are kinematics and kinetics. Kinematics deals with the motion or the outcome of the particle after the application of forces. This part studies time, displacement, velocity, and acceleration of the particle. Kinetics, on the other hand, covers the whole analysis of the forces causing motion.

The following list shows the coverage of Dynamics in a course:

• Introduction
• Particle Kinematics: Rectilinear Motion
• Particle Kinematics: Curvilinear Motion
• Particle Kinematics: Translation of Axes
• Particle Kinematics: Absolute Dependent Motion
• Kinetics of a particle: Force and Acceleration
• Kinetics of a particle: Work and Energy
• Kinetics of a particle: Impulse and Momentum
• Plane Kinematics of Rigid Bodies