MODULE 1. INTRODUCTION TO DYNAMICS

This module tackled the rectilinear motion of a particle which describes the position, velocity, and acceleration of a particle at every instant as it moves along a straight line. The general methods of analysis to study the motion of a particle in which two important particular cases, namely, the uniform motion and the uniformly accelerated motion of a particle was also discussed. Lastly, the module ended with the simultaneous motion of several particles and the concept of the relative and dependent motion of one particle with respect to another.

position, velocity, and acceleration

A particle moving along a straight line is called rectilinear motion. The straight line of the particle is usually defined using a single coordinate axis, s. The position coordinate s is used to specify the location of a particle at a given instant. s is positive if the coordinate axis is positive to the right of the origin, and negative if it is located left of the origin. The displacement of a particle is the average of the change in its position and is also called a vector quantity. Specifically, the distance traveled is a positive scalar which represents the total length of the path over which the particle travels.

Average velocity is defined as the quotient of displacement Δx and time interval Δt over the given time interval. A positive value of v indicates that the particle moves in positive direction, and negative v indicates that the particle moves in negative direction.

Similarly, negative acceleration is determined by obtaining the quotient of Δv and Δt. The instantaneous acceleration of a particle is also obtained by allowing the time interval Δt to approach zero. A positive value of a indicates that velocity increases (moving faster) in positive direction or slowly in negative direction), otherwise a will be negative. On the other hand, deceleration refers to a when speed of particle decreases or when a particle is moving more slowly.

In general, the acceleration of a particle can be expressed as a function of variables x,v, and t. The differential equations of kinematics are given by these following equations:

DETERMINING THE MOTION OF A PARTICLE

Problems concerning kinematics can be solved by first identifying the independent variable and finding what is required. With these, we have to consider these three types of motion:

The acceleration is a given function of t

The acceleration is a given function of x

The acceleration is a given function of v

uniform rectilinear motion

Uniform rectilinear motion is a type of straight line motion where the acceleration a of a particle is zero because of the constant velocity. If the particle's velocity is constant, the equation as shown in the right is used.

UNIFORMLY ACCELERATED RECTILINEAR MOTION

Uniformly accelerated rectilinear motion is another common type of motion wherein the acceleration of the particle is constant. The three kinematic equations of motion with constant acceleration is summarized into following equations shown in the left figure

MOTION OF SEVERAL PARTICLES

It is possible to derive equations of motion for particles that move independently along the same line. For example, Consider two particles A and B moving along the same straight line. If we measure the position coordinates XA and XB from the same origin, the difference XB - XA defines the relative position coordinate of B with respect to A, which is denoted by XB/A . The rate of change of XB/A is known as the relative velocity of B with respect to A and the rate of change of VB/A is known as the relative acceleration of B, with respect to A.

Relative position of two particles

Relative velocity of two particles

Relative acceleration of two particles

However, there are times where the position of a particle depends upon the position of another particle or several other particles. The method of relating the dependent motion of particle can be performed using algebraic scalars or position coordinates provided each particle moves along a rectilinear path.

Here are the relations that are satisfied by the position coordinates of two blocks, having a one degree of freedom. Thus, similar relation holds between the velocities and acceleration of the particles.

ASSIGNMENT/S SUBMITTED IN MODULE 1

Assignment#1 Part 1_BARTOLOME.pdf

Assignment #1 Part 2_BARTOLOME.pdf

COURSEWORK #1

Coursework#1_BARTOLOME.pdf

reflection

In this module, I have learned that the motion of a particle can be analyzed without considering the forces affecting the motion. Also, the kinematic discussion of particles always depend on the displacement, velocity, and acceleration. The three differential kinematic equations of motion helped me to determine what class of motion is required to solve problems in rectilinear motion. In cases where the velocity is constant, the equation for uniform rectilinear motion should be used. Likewise, for particle moving in a constant acceleration (for a straight path), I can use those three types of equations derived from continuous mathematical integration and manipulation of kinematic equations.

There are situations wherein several particles move independently and dependently. For independent motion, I can apply the equations defining relative motion of particles, and for particles that are interconnected with each other through ropes or pulleys, such problems can be solved by relating the position coordinates of several particles. If they are linear, a similar relation goes for velocity and acceleration. Lastly, Answering the classwork assignments and courseworks helped me a lot in understanding the concepts in kinematics. I was able to organize the problem well by listing first the given information for each problem and imagining a visual representation for me to correctly sketch the free body diagram. Using free body or kinetic diagram and selecting a proper coordinate system helped me to describe the motion of particles. Therefore, I can succesfully write the equations needed to solve the unknowns.

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