Derived Units

Length

Time

Mass

UNITS

The value of any physical quantity must be expressed in terms of some standard or unit. Such units are necessary for us to compare measurements and also to distinguish between different physical quantities. All physical quantities can be expressed in terms of three fundamental quantities: mass, length, and time. In the Systeme International (SI) the base units for mass, length, and time are the kilo­gram (kg), the meter (m). and the second (s). It is convenient to define additional base units: the kelvin (K) for temperature, the ampere (A) for electric current, and the candela (cd) for luminous intensity. A base unit must have a precise and reproducible standard. For the moment we consider only mass, length, and time.

The SI unit of mass, the kilogram (kg), was originally defined as the mass of one liter of water at 4 °C. Practical difficulties in obtaining pure water and the fact that this definition involved another quantity, namely temperature, led to its replace­ment. The SI unit of mass (1 kg) is now defined to be the mass of a platinum-indium cylinder kept in the International Bureau of Weights and Measures in Sevres, France.

The SI unit of time is the second (s). This was originally defined as 1/84,600 of a mean solar day. (The interval between the times at which the sun reaches the highest point in the sky on successive days is called a solar day. Because of seasonal variations and random fluctuations, the mean value over a year is taken.) Because the rate of rotation of the earth has been gradually decreasing, the mean solar day was chosen to be the value in 1900. This is hardly a reproducible standard! In 1967. the second was redefined in terms of certain radiation emitted by atoms of cesium-133. Specifically, in one second there are 9,162,631,770 vibra­tions in the radiation.

The SI unit of length is the meter (m). The meter was originally defined (in the eighteenth century) to be one ten-millionth (10⁻⁷) of the distance from the equator to the North Pole. In this century, but prior to 1960, it was defined as the distance between two fine scratches on a platinum-iridium bar stored under controlled conditions in Sevres, France. In 1983 the meter was redefined as the distance traveled by light in a vacuum in 1/299,792,458 second. This length standard, which depends on the definition of the second, effectively defines the speed of light in vacuum to be exactly 299,792,458 m/s. The speed of light has become a primary standard, and any improvement in measuring either the meter or the second is automatically reflected in the other.

The units of physical quantities other than mass, length, and time are combina­tions of the base units and are called derived units. For example, the unit of speed is m/s, for acceleration it is m/s², and for density (mass per unit volume) it is kg/m³. Sometimes a derived unit is given a special name to honor someone. For example, Newton's second law relates the acceleration a of a body of mass m to the force F acting on it: F = ma. The unit of force is kg-m/s². This combination is called the newton (N).

Дата добавления: 2014-01-05