How it works : Dynamics

DYNAMICS
Dynamics is a branch of physics concerned with moving bodies- their direction, speed, momentum and energy, and the inter-relation of these quantities. It therefore represents one side of the subject of mechanics, the other being STATICS-the study of stationary bodies, and the forces on these, in a stable, non-moving, situation. The design of a bridge, for example, requires the use of statics to determine its structural stability. Dynamics, on the other hand, being concerned with movement, seeks to determine quantitatively the effects of a force on a body's motion and as such is closely related to the subject of applied mathematics. Indeed, once the relevant laws of physics have been employed to analyze the given situation and establish the mathematical expressions of these laws, the problem becomes largely one of the manipulation and solution of equations.

Kinematics and kinetics
Dynamics is split into two subsections: kinematics and kinetics. Kinematics deals with the mathematical description of the body's motion such as its speed and velocity, and does not actually touch the physics of the situation. Once this is done, an analysis from the point of view of the laws of physics that govern motion is performed: this is the kinetics part of the investigation.

Below: some concepts in dynamics. In (A) a mass M is shown -this is a scalar quantity because it has no direction. In (B), the two cars have the same (scalar) speed but different (vector) velocities because they move in different directions. The bow in (C) converts potential (stored) energy into kinetic (motive) energy. A (vector) force on a mass produces an acceleration-this is also a vector quantity (shown in D). In rotary motion (F) torque produces angular acceleration.

History
Sir Isaac NEWTON'S LAWS of motion formulated in the seventeenth century and developed by later physicists and mathematicians were spectacularly successful in their explanations and analysis of many problems, from the motion of planets around the sun to the behaviour of tiny particles of dust. The discovery of Neptune in the mid-nineteenth century, for example, was not due to improvements in the optical properties of telescopes, but to the application of dynamics.

A dynamical analysis of the solar system had shown that the observed motions of the known planets were at variance with what was predicted theoretically. It was then realized that the existence of an eighth planet was necessary as the deviations could only be explained if there was a distant planet whose gravitational attraction was distorting the orbits of the others. The analysis even predicted where to look for this planet, its size and some details of its orbit around the sun. It was located within a couple of degrees of the calculated position by Professor Galle in Berlin in 1846, following independent calculations by Leverrier in France and Adarna in England.

Scalar and vector quantities in dynamics
In dynamics there is found first a precise definition of all the properties that bodies exhibit because they are moving-these properties are called dynamical variables and include speed, velocity, acceleration, momentum and energy.

Speed is defined as distance travelled per unit time and is a scalar quantity, meaning that it has a magnitude expressed only in units of speed such as miles per hour or metres per second. Many dynamical variables, however, are vector quantities which means that they must be assigned a direction in space as well as a magnitude.

Velocity, for example, is defined as speed in a particular direction and is a vector quantity. Thus two cars may have the same speed if they cover the same distance in the same time, but will only have the same velocity if they are travelling in the same direction (that is, parallel). Momentum is also a vector quantity because it is defined as mass multiplied by velocity and the direction of this vector is the same as the velocity vector involved in its calculation.

The momentum of a body is a measure of how difficult it is to bring it to rest. Consider two bodies, one with twice the mass of the other but the smaller mass travelling with twice the speed of the larger. They are equally difficult to stop because the doubled mass of the slower body compensates for the higher speed of the smaller mass each body has the same momentum.

Vectors are of fundamental importance because a body will only change its line of travel, or more generally, its momentum, if it is forced to do so. Just how large that force must be and exactly how quickly (and by how much) it will alter its direction is basically what dynamics is all about.

The concept of force is central to the whole theory of dynamics. Newton's laws of motion state that a body's momentum (and therefore its speed and direction of travel) can only be changed by the application of a force. The rate of change of momentum with time is determined by the magnitude of the force and the direction of change by the direction in which the force acts. Force is therefore also a vector quantity.

Energy, work and power
When a body is moving, it possesses energy, and this is called kinetic energy. This may be harnessed and put to a useful purpose. Hydroelectric power stations do just that with the energy of moving water. The water passes through turbines which 'tap' the kinetic energy of the river and turn this into electrical energy. In the process, the water is slowed down, that is, it yields part of its energy associated with its motion. To slow down a car the brakes are applied. This converts some of the kinetic energy of the moving vehicle into heat, which is dissipated by the brakes, thus slowing it down.

Above: dynamics is the science of moving bodies and the forces which produce and affect motion. The flightpath of a rocket, for example, is determined by the thrust of the motors, the earth's gravitational pull, the latitude of the launch site and air currents. These factors are fed into a computer to determine speed and position.

Another form of energy is potential energy. This is the energy that a body possesses by virtue of its position in a force field. For example, a body held above the ground has the 'potential' to fall to the ground in the Earth's gravitational field. Whilst falling it loses its potential energy but gains in speed and therefore gains kinetic energy. On reaching the ground it has no potential energy left-it no longer has any 'potential' to move. An arrow acquires potential energy when it is drawn back in a bow by virtue of the tension (force) in the string. When it is released, all this potential energy is transferred to kinetic energy.

Both potential and kinetic energy are forms of stored energy- one is stored by virtue of its position, the other by virtue of its motion. Work, on the other hand, is the amount of energy transferred to a body. It is, for example, the amount of energy imparted to a body when a force acts on it. Power is another important dynamical variable as it is the rate at which energy is transferred in time, that is, the rate of doing work. Energy, work and power are all scalar quantities because they cannot be related to a specific direction. Energy, for example, can be harnessed to do work in any direction.

Rotary motion
With linear motion the force acting on a body is equal to the mass of the body times its acceleration (Newton's laws). With a rotating body there is a similar relationship between the twisting force, or torque (from the Latin verb 'torquere'-to twist), and angular acceleration; torque is equal to the moment of INERTIA of the body (inertia is resistance to being moved) times the angular acceleration.

Dynamics and modern physics
Like so many branches of physics, dynamics had to be substantially revised in the light of modern discoveries. To explain properly the newly observed phenomena that occur on the microscopic level, such as the collisions and interactions between electrons and nuclei, Newtonian (or as it is now known, classical) mechanics is inadequate and QUANTUM mechanics is required. Also, the strange behaviour of bodies moving with speeds comparable to that of light cannot be explained by classical mechanics and relativistic mechanics becomes important. Practical applications on the scale and complexity of those found in most real-life engineering projects, however, need not resort to such advanced approaches.

Reproduced from HOW IT WORKS p823