{"id":27,"date":"2020-04-19T15:57:00","date_gmt":"2020-04-19T19:57:00","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/humanbiomechanics\/chapter\/1-2-physical-quantities-and-units-2\/"},"modified":"2020-06-03T23:24:19","modified_gmt":"2020-06-04T03:24:19","slug":"1-2-physical-quantities-and-units-2","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/humanbiomechanics\/chapter\/1-2-physical-quantities-and-units-2\/","title":{"raw":"1.2 Physical Quantities and Units.","rendered":"1.2 Physical Quantities and Units."},"content":{"raw":"
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\u00a0Mechanics is a quantitative science which means we will describe human movement and its causes using numbers. To provide information about a movement, we have to be able to specify how it is measured. For example, we define distance and time by specifying methods for measuring them, whereas we define average speed<\/em><\/em> by stating that it is calculated as distance traveled divided by time of travel.<\/p>\r\n

Measurements of physical quantities are expressed in terms of units<\/span><\/strong>, which are standardized values. For example, the length of a race, which is a physical quantity, can be expressed in units of meters (for sprinters) or kilometers (for distance runners). Without standardized units, it would be extremely difficult for scientists to express and compare measured values in a meaningful way. (See Figure 1 below.)\u00a0<\/a><\/p>\r\n\r\n

\r\n\r\n[caption id=\"attachment_5225\" align=\"aligncenter\" width=\"290\"]\"\"<\/a> Figure 1. Distances given in unknown units are maddeningly useless.[\/caption]\r\n

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There are two major systems of units used in the world: <\/span>SI units<\/strong> (also known as the metric system) and <\/span>English units<\/strong> (also known as the customary or imperial system). <\/span>English units<\/strong> were historically used in nations once ruled by the British Empire and are still widely used in the United States. Virtually every other country in the world now uses SI units as the standard; the metric system is also the standard system agreed upon by scientists and mathematicians. The acronym \u201cSI\u201d is derived from the French <\/span>Syst\u00e8me International<\/em>.<\/span>\r\n

SI Units: Fundamental and Derived Units<\/span><\/h1>\r\n

The metric or SI system is administered in France by the Bureau International des Poids and Mesures or BIPM.\u00a0 \u00a0You can read more about them at\u00a0\u00a0https:\/\/www.bipm.org\/en\/about-us\/<\/a><\/p>\r\nTable 1 below shows the fundamental SI units that are used throughout this textbook.\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
Length<\/th>\r\nMass<\/th>\r\nTime<\/strong><\/th>\r\n<\/th>\r\n<\/tr>\r\n<\/thead>\r\n
meter (m)<\/td>\r\nkilogram (kg)<\/td>\r\nsecond (s)<\/td>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n
Table 1.<\/strong> Fundamental SI Units.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n \r\n

It is an intriguing fact that some physical quantities are more fundamental than others and that the most fundamental physical quantities can be defined only<\/em><\/em> in terms of the procedure used to measure them. The units in which they are measured are thus called fundamental units<\/span><\/strong>. In this textbook, the fundamental physical quantities are taken to be length, mass and time. All other physical quantities, such as force and velocity, can be expressed as algebraic combinations of length, mass and time; these units are called derived units<\/span><\/strong>.<\/p>\r\n\r\n<\/section>

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Units of Time, Length, and Mass: The Second, Meter, and Kilogram<\/h1>\r\n

The Second<\/h2>\r\n
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The SI unit for time, the second <\/span>(abbreviated s), has a long history. For many years it was defined as 1\/86,400 of a mean solar day. More recently, a new standard was adopted to gain greater accuracy and to define the second in terms of a non-varying, or constant, physical phenomenon (because the solar day is getting longer due to very gradual slowing of the Earth\u2019s rotation).<\/p>\r\n\r\n<\/section>\r\n

The Meter<\/h2>\r\n
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The SI unit for length is the meter<\/span> (abbreviated m); its definition has also changed over time to become more accurate and precise. In 1983, the meter was given its present definition (partly for greater accuracy) as the distance light travels in a vacuum in 1\/299,792,458 of a second. \u00a0This change defines the speed of light to be exactly 299,792,458 meters per second. The length of the meter will change if the speed of light is someday measured with greater accuracy.<\/p>\r\n\r\n<\/section>

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<\/figcaption>\r\n\r\n[caption id=\"\" align=\"aligncenter\" width=\"400\"]\"Beam Figure 2.<\/strong> The meter is defined to be the distance light travels in 1\/299,792,458 of a second in a vacuum. Distance traveled is speed multiplied by time.[\/caption]<\/figure>\r\n

The Kilogram<\/h2>\r\n
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The SI unit for mass is the kilogram<\/span> (abbreviated kg); it is defined to be the mass of a platinum-iridium cylinder kept with the old meter standard at the International Bureau of Weights and Measures near Paris.<\/p>\r\nIn Biomechanics, all pertinent physical quantities can be expressed in terms of these fundamental units of length, mass, and time.\r\n\r\n<\/section>\r\n

Metric Prefixes<\/h2>\r\n<\/section><\/section>
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SI units are part of the metric system<\/span><\/strong>. The metric system is convenient for scientific and engineering calculations because the units are categorized by factors of 10. The table below gives metric prefixes and symbols used to denote various factors of 10.<\/p>\r\n

Metric systems have the advantage that conversions of units involve only powers of 10. There are 100 centimeters in a meter, 1000 meters in a kilometer, and so on.<\/p>\r\n\r\n

\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
Prefix<\/th>\r\nSymbol<\/th>\r\nValue<\/th>\r\nExample (some are approximate)<\/th>\r\n<\/tr>\r\n<\/thead>\r\n
kilo<\/strong><\/td>\r\nk<\/strong><\/td>\r\n103<\/sup><\/strong><\/td>\r\nkilometer<\/strong><\/td>\r\nkm<\/td>\r\n103<\/sup> m<\/td>\r\nabout 6\/10 mile<\/td>\r\n<\/tr>\r\n
hecto<\/td>\r\nh<\/td>\r\n102<\/sup><\/td>\r\nhectoliter<\/td>\r\nhL<\/td>\r\n102<\/sup> L<\/td>\r\n26 gallons<\/td>\r\n<\/tr>\r\n
deka<\/td>\r\nda<\/td>\r\n101<\/sup><\/td>\r\ndekagram<\/td>\r\ndag<\/td>\r\n101<\/sup> g<\/td>\r\nteaspoon of butter<\/td>\r\n<\/tr>\r\n
\u2014<\/td>\r\n\u2014<\/td>\r\n100<\/sup><\/strong>\r\n\r\n(=1)<\/td>\r\nmeter<\/strong><\/td>\r\n<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n
deci<\/td>\r\nd<\/td>\r\n10-1<\/sup><\/td>\r\ndeciliter<\/td>\r\ndL<\/td>\r\n10-1<\/sup> L<\/td>\r\nless than half a soda<\/td>\r\n<\/tr>\r\n
centi<\/strong><\/td>\r\nc<\/strong><\/td>\r\n10-2<\/sup><\/strong><\/td>\r\ncentimeter<\/strong><\/td>\r\ncm<\/td>\r\n10-2<\/sup> m<\/td>\r\nfingertip thickness<\/td>\r\n<\/tr>\r\n
milli<\/strong><\/td>\r\nm<\/strong><\/td>\r\n10-3<\/sup><\/strong><\/td>\r\nmillimeter<\/strong><\/td>\r\nmm<\/td>\r\n10-3<\/sup> m<\/td>\r\nflea at its shoulders<\/td>\r\n<\/tr>\r\n
Table 2.<\/strong> Select Metric Prefixes for Powers of 10 and their Symbols.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/section>
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\r\n\r\nPhysical quantities are a characteristic or property of an object that can be measured or calculated from other measurements.\r\n