Derivation Of The Gravitational Force

Newton derived the gravitational force law from his three laws of motion, together with certain thought experiments and data reflecting the motion of the Moon relative to the Earth. As they are illuminating, we reproduce some of Newton's arguments, phrasing them in modern language. The actual motion of the Moon around the Earth is quite complicated due to gravitational interactions with the Sun and other nearby planets. As a reasonable first approximation, however, the Moon's orbit is roughly...

Instantaneous Rate Of Change

Instantaneous rate of change is one of the most fundamental concepts in physics. The rate of change of the position of an object is called the velocity. Normally, one speaks of velocity in a certain direction, but when there is only one direction, the velocity is described by a single number called the speed and corresponds to the reading on a car's speedometer. Let t denote the number of seconds from the time that one has thrown a baseball straight up from the Earth's surface. Let x(t) denote...

Slope And Rate Of Change

Now consider a completely general function, f f(t), which depends on an independent variable t, which we will think of as time. We will use the Greek letter delta (8), to mean change in, which saves a lot of writing. Consider a very small change in time the concretely minded reader may think that 8t 0.0001 sec throughout this discussion, although the arguments are general. Note that above, the variable h played the role of a change in time, so we will make the replacement h 8t in what follows....

Newtons Laws Of Motion

Newton's laws of motion, together with Newton's law of universal gravitation and the mathematical techniques of calculus, provided for the first time a unified explanation for a wide range of physical phenomena, most of which had been studied by scientists and philosophers before Newton, who had come to various partial, incorrect, or approximate solutions. The phenomena for which Newton's theory works well include the motion of spinning bodies motion of bodies in fluids projectile motion...

Physics History Legend And Folklore

This section is dedicated to a brief, informal history of the attempts by our predecessors to understand the motions of planets, stars, and galaxies, which ultimately culminated in Isaac Newton's invention of calculus and of the associated theory of physics now known as Newtonian mechanics. Newton's mechanics included the first modern concept of force and the rules by which forces influence the motion of bodies. We will give a brief, modernized account of Newton's ideas in Chapter 2. Newton...