Atwood's Machine, an instrument for illustrating the relations of time, space, and velocity in the motion of a body falling under the action of gravity. It was invented by George Atwood or Attwood, a mathematician of some eminence, who was born in 1745, educated at Cambridge, became fellow and tutor of Trinity College in that university, published a few treatises on Mechanics and Engineering, and died in 1807. It is found that a body falling freely, passes through 16 feet in the first second, 64 feet in the first two seconds, 144 feet in the first three seconds, and so on. Now, as these spaces are so large, we should require a machine of impracticable size to illustrate the relations just mentioned. The object of Atwood's machine is to reduce the scale on which gravity acts without in any way altering the nature of its actions. The machine consists essentially of a pulley, P (see fig. 1), moving on its axis with very little friction, with a fine silk cord passing over it, sustaining two equal cylindrical weights, p and q, at its extremities. The pulley rests on a square wooden pillar, graduated on one side in feet and inches, which can be placed in a vertical position by the levelling-screws of the sole on which it stands. Two stages, A and B, slide along the pillar, and can be fixed at any part of it by means of fixing-screws. One of these stages, A, has a circular hole cut into it, so as to allow the cylinder, p, to pass freely through it; the other is unbroken, and intercepts the passage of the weight. A series of smaller weights, partly bar-shaped, partly circular, may be placed on the cylinders in the way represented in figs. 2 and 3. A pendulum usually accompanies the machine, to beat seconds of time. The weights of the cylinders, p and q, being equal, they have no tendency to rise or fall.
When a bar is placed on p, the motion that ensues is due only to the action of gravity upon it, so that the motion of the whole must be considerably slower than that of the bar falling freely. Suppose, for instance, that p and q are each ounces, and that the bar is 1 ounce, the force acting on the system—leaving the friction and inertia of the pulley out of account—would be of gravity, or the whole would move only 1 foot in the first second, instead of 16. If the bar be left free to fall, its weight would bring its own mass through 16 feet the first second; but when placed on p, this force is exerted not only on the mass of the bar, but on that of p and q, which is 15 times greater, so that it has altogether 16 times more matter in the second case to move than in the first, and must, in consequence, move it 16 times more slowly. By a proper adjustment of weights, the rate of motion may be made as small as we please. The various formulæ (see KINEMATICS) connecting time, speed, and space fallen through under gravity can be experimentally verified by such an instrument. For example, if the weight of p be increased by a small amount, and the space it falls through in one second be noted, it is found that after two seconds it has fallen through four times that space, and so on. Thus, the space fallen through from rest is proportional to the square of the time occupied in falling.