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Introduction to Dynamics Dynamics is that branch of mechanics which deals with the motion of bodies under the action of forces. Dynamics has two distinct parts: kinematics and kinetics. Kinematics is the study of motion without reference to the forces which cause motion. Kinetics relates the action of forces on bodies to their resulting motions. When machines and structures started to operate with high speeds it became necessary to make calculations based on the principles of dynamics rather than on the principles of statics. The rapid technological developments of the present day require increasing application of the principles of mechanics. These principles are basic to the analysis and design of moving structures, fixed structures subjected to shock loads, robotic devices, automatic control systems, rockets and machinery of all types. BASIC CONCEPTS The basic concepts in mechanics are space, time, mass and force. Among these, space, time, mass are absolute quantities, which mean that they are independent of each other and cannot be expressed in terms of other quantities or in simpler terms. Force, on the other hand, is a derived quantity. Space (uzay) is the geometric region occupied by bodies. Position in space is specified by linear or angular measurements with respect to a geometric reference system. In Newtonian Mechanics the basic reference system is named as the “primary inertal system” (birincil mutlak sistem) and it is a virtual system assumed as neither rotating or translating in space. For the examination of motion occurring on or near Earth, it is suitable to use a reference system attached to Earth as the primary inertial system. Time (zaman) is a measure of the succession of events and is considered an absolute quantity in Newtonian mechanics. Mass (kütle) is the quantitative measure of the inertia or resistance to change in motion of a body. Mass can also be considered as the amount of matter within a body. Although the mass of a body is an absolute quantity, its weight can change depending on the gravitational force (W=mg). Force (kuvvet) is the action of one body on another. A force possesses both magnitude and direction, therefore it is a vector quantity. A particle (parçacık veya maddesel nokta) is a body of negligible dimensions. Generally a particle is thought to be an infinitesimally small element which possesses all properties of a body. But when the dimensions of a body are irrelevant to the description of its motion or the action of forces on it, a large body may also be treated as a particle. A particle has mass but no shape and dimensions. The body is considered to be concentrated at a single point which usually will be its mass center. All the forces acting on the body will have to pass from this point, i.e. the forces will be concurrent. Some examples to particles are shown here; a ball, a block, even an airplane can be considered as particles. A rigid body (rijit veya katı cisim) is a body whose changes in shape are negligible compared with the overall dimensions of the body or with the changes in position of the body as a whole. The shape and dimensions of a rigid body will remain the same under all conditions of loading and at all times. Some examples of rigid bodies are shown here. Displacement (Yer Değiştirme) Time rate of change of position coordinates. Displacement is a vector quantity. Examination of displacement is carried out by means of a suitable coordinate system. The selected coordinate system can either be an absolute (fixed) or a moving system. Trajectory / Path (Yörünge) It is a line or a curve obtained when all the points a body occupies within a specific time period are joined. Kinematics (Kinematik) Observes motion without considering the forces that cause the motion. In other words, it deals with the geometry of motion. It constitutes relationships between path, velocity, acceleration and time. Kinetics (Kinetik) Observes motion by considering the forces that cause the motion. In this field, in addition to the quantities in kinematics, forces and / or moments, together with mass also take part in relationships. NEWTON’S LAWS The laws which constitute the basis of engineering mechanics are formulated in 1687 by Sir Isaac Newton. These are: Law I. (Equation of Equilibrium) A particle remains at rest or continues to move with uniform velocity (along a straight line with a constant speed) if there is no unbalanced force acting on it. F 0 NEWTON’S LAWS Law II. (Equation of Motion)The acceleration of a particle is proportional to the resultant force acting on it and is in the direction of this force. F ma m F ma kg 2 Newton (N ) s NEWTON’S LAWS Law III. (Principle of Action and Reaction) The forces of action and reaction between interacting bodies are equal in magnitude, opposite in direction, and collinear. F G m1m2 r2 GRAVITATION Newton’s law of gravitation, which governs the mutual attraction between bodies, is stated as m1 m 2 FG 2 r Gm m= a universal constant called the constant of gravitation F G 1 2 r2 G 6.673 10 11 m3 kg s2 F r2 N m2 kg m m 2 m3 G 2 m1m 2 kg kg s kg kg kg s 2 UNITS The International System of metric units (SI) is defined and used in this lecture. Units Quantity Mass Time Length Force Symbol F ma m t L F Unit kg s m N (kilogram) (second) (meter) (Newton)