Standards of Length, Mass, and Time
TABLE 1.1 Approximate Values of Some Measured Lengths
Length (m) Distance from the Earth to most remote known quasar Distance from the Earth to most remote known normal galaxies Distance from the Earth to nearest large galaxy (M 31, the Andromeda galaxy) Distance from the Sun to nearest star (Proxima Centauri) One lightyear Mean orbit radius ofthe Earth about the Sun Mean distance from the Earth to the Moon Distance from the equator to the North Pole Mean radius of the Earth Typical altitude (above the surface) of a satellite orbiting the Earth Length of a football ﬁeld Length of a houseﬂy Size of smallest dust particles Size of cells of most living organisms Diameter of a hydrogen atom Diameter of an atomic nucleus Diameter of a proton1.4 9 2 4 9.46 1.50 3.84 1.00 6.37 2 9.1 5 10 10 10 10 10 1026 1025 1022 1016 1015 1011 108 107 106 105 101 10 3
4 5 10 14 15
The basic SI unit of mass, the kilogram (kg), is deﬁned as the mass of a speciﬁc platinum – iridium alloy cylinder kept at the International Bureau of Weights and Measures at Sèvres, France. This mass standard was established in 1887 and has not been changedsince that time because platinum – iridium is an unusually stable alloy (Fig. 1.1a). A duplicate of the Sèvres cylinder is kept at the National Institute of Standards and Technology (NIST) in Gaithersburg, Maryland. Table 1.2 lists approximate values of the masses of various objects.
Visit the Bureau at www.bipm.fr or the National Institute of Standards at www.NIST.gov
TimeBefore 1960, the standard of time was deﬁned in terms of the mean solar day for the 1 1 1 year 1900.2 The mean solar second was originally deﬁned as (60)(60)(24) of a mean solar day. The rotation of the Earth is now known to vary slightly with time, however, and therefore this motion is not a good one to use for deﬁning a standard. In 1967, consequently, the second was redeﬁned to take advantage ofthe high precision obtainable in a device known as an atomic clock (Fig. 1.1b). In this device, the frequencies associated with certain atomic transitions can be measured to a precision of one part in 1012. This is equivalent to an uncertainty of less than one second every 30 000 years. Thus, in 1967 the SI unit of time, the second, was redeﬁned using the characteristic frequency of a particularkind of cesium atom as the “reference clock.” The basic SI unit of time, the second (s), is deﬁned as 9 192 631 770 times the period of vibration of radiation from the cesium-133 atom.3 To keep these atomic clocks — and therefore all common clocks and
Masses of Various Bodies (Approximate Values)
Body Visible Universe Milky Way galaxy Sun Earth Moon Horse Human Frog Mosquito Bacterium Hydrogenatom Electron Mass (kg) 1052 7 1.99 5.98 7.36 1041 1030 1024 1022
103 102 10 1 10 5 10 15 1.67 10 9.11 10
One solar day is the time interval between successive appearances of the Sun at the highest point it reaches in the sky each day. Period is deﬁned as the time interval needed for one complete vibration.
Standards of Length, Mass, and Time
TABLE 1.3Approximate Values of Some Time Intervals
Interval (s) Age of the Universe Age of the Earth Average age of a college student One year One day (time for one rotation of the Earth about its axis) Time between normal heartbeats Period of audible sound waves Period of typical radio waves Period of vibration of an atom in a solid Period of visible light waves Duration of a nuclear collision Time for lightto cross a proton 5 1.3 6.3 3.16 8.64 8 10 10 10 10 10 10 1017 1017 108 107 104 10 1
3 6 13 15 22 24
time are the foot (ft), slug, and second, respectively. In this text we shall use SI units because they are almost universally accepted in science and industry. We shall make some limited use of British engineering units in the study of classical mechanics. In addition to the basic SI units...