Additional texts

Read the texts and translate them in written form.

MOTION

Motion is the change of position of a body relative to another body or with respect to a frame of reference or a coordinate system. All motions take place on definite paths, and the nature of these paths determines the character of the motions. If all points in a body have similar but not necessarily straight paths relative to another body, the first body has motion of translation relative to the second body. If the paths are straight, it is called rectilinear translation. In both cases all points in the body have the same velocity (directed speed) and the same acceleration (time rate of change of velocity).

If all points in a body have different paths on another body, the motion of the first body relative to the second is a combination of translation and rotation. Rotation occurs when any line on a body changes its orientation relative to a line on another body. For example, on a reciprocating engine, one end of the connecting rod is attached by a hinge-type joint (the wrist pin) to the piston and moves with it on a straight path relative to the cylinder block, while the other end of the rod is attached by a hinge-type joint (the crankpin) to the crankshaft and moves with it on a circular path relative to the block.

Bodies connected by hinges can only rotate relative to one another. Consequently, the motion of the connecting rod relative to the piston and relative to the crankshaft is pure rotation. Relative to the block, the motion is a combination of translation and rotation, which is the most general type of plane motion--i.e., motion in parallel planes relative to the block.

All motions are relative, but the term relative motion is usually reserved for motion relative to a moving body--i.e., motion on a moving path. Strictly speaking, Newton's laws of motion are valid only for motions on paths that are fixed to the centre of the solar system. These are known as absolute paths, and, because the Earth rotates and moves around the Sun, motion relative to the Earth is not absolute motion. In most cases, however, the effects of the Earth's motion on calculations involving Newton's laws are small and can be neglected. Motions relative to the Earth or to any body that is fixed to the Earth are assumed to be absolute.

In addition to rotating about moving axes, like the connecting rod, or about a fixed axis, like the crankshaft, a body can also rotate about a fixed point. This is the type of motion that a spinning top executes.

Velocity

Velocity is a quantity that designates how fast and in what direction a point is moving. As it has direction as well as magnitude, velocity is known as a vector quantity and cannot be specified completely by a number, as can be done with time or length, which are scalar quantities. Like all vectors, velocity is represented graphically by a directed line segment (arrow) the length of which is proportional to its magnitude.

A point always moves in a direction that is tangent to its path; for a circular path, for example, its direction at any instant is perpendicular to a line from the point to the centre of the circle (a radius). The magnitude of the velocity (i.e., the speed) is the time rate at which the point is moving along its path.

If a point moves a certain distance along its path in a given time interval, its average speed during the interval is equal to the distance moved divided by the time taken. A train that travels 100 km in 2 hours, for example, has an average speed of 50 km per hour.

During the two-hour interval, the speed of the train in the previous example may have varied considerably around the average. The speed of a point at any instant may be approximated by finding the average speed for a short time interval including the instant in question. The differential calculus, which was invented by Isaac Newton for this specific purpose, provides means for determining exact values of the instantaneous velocity.

MASS

Mass is a quantitative measure of inertia, a fundamental property of all matter. It is, in effect, the resistance that a body of matter offers to a change in its speed or position upon the application of a force. The greater the mass of a body, the smaller the change produced by an applied force. Although mass is defined in terms of inertia, it is conventionally expressed as weight. By international agreement the standard unit of mass, with which the masses of all other objects are compared, is a platinum-iridium cylinder of one kilogram.

Weight, though related to mass, nonetheless differs from the latter. Weight essentially constitutes the force exerted on matter by the gravitational attraction of the Earth, and so it varies from place to place. In contrast, mass remains constant regardless of its location under ordinary circumstances. A satellite launched into space, for example, weighs increasingly less the further it travels away from the Earth. Its mass, however, stays the same.

For years it was assumed that the mass of a body always remained invariable. This notion, expressed as the theory of conservation of mass, held that the mass of an object or collection of objects never changes, no matter how the constituent parts rearrange themselves. If a body split into pieces, it was thought that the mass divided with the pieces, so that the sum of the masses of the individual pieces would be equal to the original mass. Or, if particles were joined together, it was thought that the mass of the composite would be equal to the sum of the masses of the constituent particles. But this is not true.

With the advent of the special theory of relativity by Einstein in 1905, the notion of mass underwent a radical revision. Mass lost its absoluteness. The mass of an object was considered equivalent to energy, interconvertible with energy, and it increased significantly at exceedingly high speeds near that of light (about 3 10 metres per second, or 186,000 miles per second). The total energy of an object was understood to comprise its rest mass as well as its increase of mass caused by high speed. It was discovered that the mass of an atomic nucleus was measurably smaller than the sum of the masses of its constituent neutrons and protons. Mass was no longer considered constant, or unchangeable. The new conservation principle is the conservation of mass-energy.