NEWTON'S LAWS OF MOTION

relations between the forces acting on a body and the motion of the body, which, although formulated for the first time in usable form by Isaac Newton, had been discovered experimentally by Galileo about four years before Newton was born. The laws cover only the overall motion of a body; i.e., the motion of its centre of mass. This concept is equivalent to assuming that the body is a particle with a definite mass but no size. Strictly speaking, the laws are valid only for motions relative to a reference frame (coordinate system) attached to the fixed stars. Such a reference frame is known as a Newtonian, Galilean, or an inertial frame. Because the Earth rotates, a reference frame attached to the Earth is not inertial, and in some cases this rotation must be considered when applying Newton's laws. In most applications, however, the Earth's rotation can be neglected. Newton's first law states that, if a body is at rest or moving at a constant speed in a straight line, it will remain at rest or keep moving in a straight line at constant speed unless it is acted upon by a force. This postulate is known as the law of inertia, and it is basically a description of one of the properties of a force: its ability to change rest into motion or motion into rest or one kind of motion into another kind. Before Galileo's time it was thought that bodies could move only as long as a force acted on them and that in the absence of forces they would remain at rest. Those who sought to find the forces that kept the planets moving failed to realize that no force was necessary to keep them moving at a practically uniform rate in their orbits; gravitational force, of which they had no conception, only changes the direction of motion. Newton's second law is a quantitative description of the changes that a force can produce in the motion of a body. It states that the time rate of change of the velocity (directed speed), or acceleration, a, is directly proportional to the force F and inversely proportional to the mass m of the body; i.e., a = F / m or F = ma; the larger the force, the larger the acceleration (rate of change of velocity); the larger the mass, the smaller the acceleration. Both force and acceleration have direction as well as magnitude and are represented in calculations by vectors (arrows) having lengths proportional to their magnitudes. The acceleration produced by a force is in the same direction as the force; if several forces act on a body, it is their resultant (sum), obtained by adding the vectors tail-to-tip, that produces the acceleration. The second law is the most important, and from it all of the basic equations of dynamics can be derived by procedures developed in the calculus. A simple case is a freely falling body. Neglecting air resistance, the only force acting on the body is its weight acting down, and it produces a downward acceleration equal to the acceleration of gravity, symbolized as g, which has an average value of 9.8 metres (32.2 feet) per second per second near the surface of the Earth. Newton's third law states that the actions of two bodies upon each other are always equal and directly opposite; i.e., reaction is always equal and opposite to action. The proposition seems obvious for two bodies in direct contact; the downward force of a book on a table is equal to the upward force of the table on the book. It is also true for gravitational forces; a flying airplane pulls up on the Earth with the same force that the Earth pulls down on the airplane. The third law is important in statics (bodies at rest) because it permits the separation of complex structures and machines into simple units that can be analyzed individually with the least number of unknown forces. At the connections between the units, the force in one member is equal and opposite to the force in the other member. The third law may not hold for electromagnetic forces when the bodies are far apart.