Other Units in Physics Help (page 2)
Introduction to Other Units in Physics
The preceding seven units can be combined in various ways, usually as products and ratios, to generate many other units. Sometimes these derived units are expressed in terms of the base units, although such expressions can be confusing (for example, seconds cubed or kilograms to the –1 power). If you see combinations of units in a physics book, article, or paper that don’t seem to make sense, don’t be alarmed. You are looking at a derived unit that has been put down in terms of base units.
The standard unit of plane angular measure is the radian (rad). It is the angle subtended by an arc on a circle whose length, as measured on the circle, is equal to the radius of the circle as measured on a flat geometric plane containing the circle. Imagine taking a string and running it out from the center of a circle to some point on the edge and then laying that string down around the periphery of the circle. The resulting angle is 1 rad. Another definition goes like this: One radian is the angle between the two straight edges of a slice of pie whose straight and curved edges all have the same length r (Fig. 6-4). It is equal to about 57.2958 angular degrees .
The Angular Degree
The angular degree, symbolized by a little elevated circle (°) or by the three-letter abbreviation deg, is equal to 1/360 of a complete circle. The history of the degree is uncertain, although one theory says that ancient mathematicians chose it because it represents approximately the number of days in the year. One angular degree is equal to approximately 0.0174533 radians.
The standard unit of solid angular measure is the steradian , symbolized sr. A solid angle of 1 sr is represented by a cone with its apex at the center of a sphere and intersecting the surface of the sphere in a circle such that, within the circle, the enclosed area on the sphere is equal to the square of the radius of the sphere. There are 4π, or approximately 12.56636, steradians in a complete sphere.
The standard unit of mechanical force is the newton , symbolized N. One newton is the amount of force that it takes to make a mass of 1 kg accelerate at a rate of one meter per second squared (1 m/s 2 ). Jet or rocket engine propulsion is measured in newtons. Force is equal to the product of mass and acceleration; reduced to base units in SI, newtons are equivalent to kilogram-meters per second squared (kg · m/s 2 ).
The standard unit of energy is the joule , symbolized J. This is a fairly small unit in real-world terms. One joule is the equivalent of a newton-meter (n · m). If reduced to base units in SI, the joule can be expressed in terms of unit mass multiplied by unit distance squared per unit time squared:
1 J = 1 kg · m 2 /s 2
The standard unit of power is the watt , symbolized W. One watt is equivalent to one joule of energy expended for one second of time (1 J/s). In fact, power is a measure of the rate at which energy is produced, radiated, or consumed. The expression of watts in terms of SI base units begins to get esoteric, as you have been warned:
1 W = 1 kg · m 2 /s 3
The standard unit of electric charge quantity is the coulomb , symbolized C. This is the electric charge that exists in a congregation of approximately 6.241506 × 10 18 electrons. It also happens to be the electric charge contained in that number of protons, antiprotons, or positrons (antielectrons). When you walk along a carpet with hard-soled shoes in the winter or anywhere the humidity is very low, your body builds up a static electric charge that can be expressed in coulombs (or more likely a fraction of one coulomb). Reduced to base units in SI, one coulomb is equal to one ampere-second (1 A · s).
The standard unit of electrical potential or potential difference , also called electromotive force (emf), is the volt , symbolized V. One volt is equivalent to one joule per coulomb (1 J/C). The volt is, in real-world terms, a moderately small unit of electrical potential. A standard dry cell of the sort you find in a flashlight (often erroneously called a battery ), produces about 1.5 V. Most automotive batteries in the United States produce between 12 and 13.5 V.
The standard unit of electrical resistance is the ohm , symbolized by the uppercase Greek letter omega (Ω). When one volt is applied across a resistance of ohm, the result is one ampere of current flow. The ohm is thus equivalent to one volt per ampere (V/A).
The standard unit of electrical conductance is the siemens , symbolized S. It was formerly called the mho , and in some papers and texts you’ll still see this term. Conductance is the reciprocal of resistance. One siemens can be considered the equivalent of one ampere per volt (A/V). If R is the resistance of a component in ohms and G is the conductance of the component in Siemens, then
G = 1/ R
R = 1/ G
The standard unit of frequency is the hertz , symbolized Hz. It was formerly called the cycle per second or simply the cycle . The hertz is a small unit in the real world, and 1 Hz represents an extremely low frequency. Usually, frequency is measured in thousands, millions, billions, or trillions of hertz. These units are called kilohertz (kHz), megahertz (MHz), gigahertz (GHz), and terahertz (THz), respectively. In terms of SI units, the hertz is mathematically simple, but the concept is esoteric for some people to grasp: It is an inverse second (s −1 ) or per second (/s).
The standard unit of capacitance is the farad , which is symbolized F. The farad is equivalent to one coulomb per volt (1 C/V). This is a large unit in real-world applications. Most values of capacitance that you will find in electrical and electronic circuits are on the order of millionths, billionths, or trillionths of a farad. These units are called microfarads (μF), nano-farads (nF), and picofarads (pF).
The standard unit of inductance is the henry , symbolized H. One henry is equivalent to one volt-second per ampere (V · s/A or V · s · A −1 ). This is a large unit in practice but not quite as gigantic as the farad. In electrical and electronic circuits, most values of inductance are on the order of thousandths or millionths of a henry. These units are called millihenrys (mH) and microhenrys (μH).
The standard unit of magnetic flux is the weber , symbolized Wb. This is a large unit in practical applications. One weber is equal to one ampere-henry (1 A · H). This is represented in the real world as the amount of magnetism produced by a constant direct current of 1 A flowing through a coil having an inductance of 1 H.
The standard unit of magnetic flux density is the tesla , symbolized T. One tesla is equivalent to one weber per meter squared (1 Wb/m 2 or Wb · m −2 ) when the flux is perpendicular to the surface under consideration. Sometimes magnetic flux density is spoken of in terms of the number of “lines of flux” per unit cross-sectional area; this is an imprecise terminology unless we are told exactly how much magnetic flux is represented by a line.
Practice problems of these concepts can be found at: Units And Constants Practice Test
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