INTRODUCTION TO DYNAMICS Engineering mechanics may be defined as the science which considers the effects of forces on rigid bodies. The subject divides naturally into two parts: statics and dynamics. In statics, we consider the effects and distribution of forces on rigid bodies which are and remain at rest, or of having constant velocity. In dynamics, we consider the motion of rigid bodies caused by the forces acting upon them. Historically, the principles of dynamics developed when it was possible to make an accurate measurement of time. Galileo Galilei (1564-1642) was one of the first major contributors to this field. His work consisted of experiments using pendulums and falling bodies. The most significant contributions in dynamics, however, were made by Isaac Newton (1642-1727), who is noted for his formulation of the three fundamental laws of motion and the law of universal gravitational attraction. Shortly after these laws were postulated, important techniques for their application were developed by Euler, D'Alembert, Lagrange, and others. BRANCHES OF DYNAMICS KINEMATICS is the geometry of motion. The term is used to define the motion of a particle or body without consideration of the forces causing the motion. Kinematics is essentially a treatment of the relations between displacement, velocity, and acceleration. KINETICS is the study of bodies with reference to the force which cause the motion. It is the study of the relationship between the forces acting on a body, the mass of the body and its motion. FUNDAMENTAL CONCEPTS IN DYNAMICS Space We view space as the environment in which objects move, and we consider it to be a collection of locations or points. The position of a point in space is indicated by specifying the point’s coordinates relative to a chosen coordinate system. Time We view time as a scalar variable that allows us to specify when an event occurs and to order a sequence of events. In classical mechanics, the most important assumption regarding time is that time is absolute. Specifically, we assume that the duration of an event is independent of the motion of the observer making time measurements and that the same clock can be used by all observers. Einstein’s theory of relativity rejects this assumption. Force The force acting on an object is the interaction between that object and its environment. A more precise description of this interaction requires that we know something about the interaction in question. For example, if two objects collide or slide against one another, we say that they interact via contact forces. Regardless of the type, a force has two essential characteristics: (1) magnitude and (2) direction. Therefore, we use vectors to mathematically represent forces. Mass The mass of an object is a measure of the amount of matter in the object. Along with the concept of force, the concept of mass has been recognized as a primitive concept, i.e., not explainable via more elementary ideas. Inertia Inertia is commonly understood as a body’s resistance to changing its state of motion in response to the application of a force system. We use inertia as an umbrella term encompassing both the idea of mass and that of mass distribution over a region of space. We call inertia properties of an object the object’s mass and a quantitative description of the mass distribution. Particle In particle mechanics, a particle is an object whose mass is concentrated at a point and therefore is also called a point mass. The inertia properties of a particle consist of only the particle’s mass. A particle is generally understood to have zero volume. Rigid Body A rigid body is the other model of real physical objects that we consider. A rigid body is an object whose mass is (1) distributed over a region of space and (2) such that the distance between any two points on it never changes. Since its mass is not concentrated at a point, the rigid body is the simplest model for the study of motions that include the possibility of rotation, i.e., a change in orientation relative to a chosen reference object. We model objects as rigid bodies when we want to account for the possibility of rotation while neglecting the effects of deformation. Finally, the mass distribution of a rigid body does not change relative to an observer moving with the body. MOTION A body is said to be in motion if it changes its position with respect to a reference point and time. The motion of a particle along a straight-line path is called rectilinear motion. The motion of a particle along a curved path is called curvilinear motion. If the moving particle describes equal distances in equal periods of time, however small, the motion is said to be uniform. If unequal distances are described by the moving point in equal periods of time, the motion is said to be non-uniform or variable. TYPES OF RECTILINEAR MOTION UNIFORM RECTILINEAR MOTION – When an object travels at a constant speed with zero acceleration. UNIFORMLY ACCELERATED RECTILINEAR MOTION – When an object travels with constant acceleration. RECTILINEAR MOTION WITH NON-UNIFORM ACCELERATION – When an object travels at an irregular speed and acceleration.
