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Appendix AA B B R E V I A T I O N S ,C O N S T A N T S ,C O N V E R S I O N S , A N DIDENTITIES

477

Electromechanical Motion Devices, Second Editionby Paul Krause, Oleg Wasynczuk and Steven PekarekCopyright 2012 Institute of Electrical and Electronics Engineers, Inc.

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Termalternating currentampereampere-turncoulombdirect currentelectromotive forcefootgaussgramhenryhertzhorsepowerinchjoulekilogramkilovarkilovoltkilovoltamperekilowattmagnetomotive forcemaxwellmegawattmetermicrofaradmillihenrynewtonnewton meteroerstedpoundpoundalpower factorpulse-width modulationradianrevolution per minuteroot mean squaresecondVoltampere reactivevoltVoltampere

AbbreviationacAAtCdcemfftGgHHzhpinJkgkvarkVkVAkWmmfMxM WmfiFmHNN - mOelbpdlpfP W Mradr/min (rpm)rm ssvarVVA

watt WWbeber

APPENDIX A

480

480

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ABBREVIATIONS, CONSTANTS, CONVERSIONS, AND IDENTITIES 479

C o n s t a n t s a n d C o n v e r s i o npermeability of free spacepermittivity of free spaceacceleration of gravitylengthmassforcetorqueenergypowermoment of inertiamagnetic fluxmagnetic flux densitymagnetizing force

Factors/ i0 = 4TT x 10" 7 W b / A me0 = 8.854 x 10"

12C

2/ N m

2

g = 9.807 m/s 21 m = 3.218 ft - 39.37 in1 kg = 0.0685 slug = 2.205 lb (mass)1 N = 0.225 lb = 3.6 oz1 N m - 0.738 lb ft1 J (W s) = 0.738 lb ft1 W = 1.341 x 10~3 hp1 kg m 2 - 0.738 slug ft2 = 23.7 lb ft21 Wb = 10 8 Mx (lines)1 W b / m 2 - 10,000 G = 64.5 kline s/in 21 At/m = 0.0254 At/in = 0.0126 Oe

T r i g o n o me t r i c I d e n t i t i e s1-1) e^a = cos a + j sin a1-2) acosrr + bsinx = \/a2 + b2 cos(x + 0) = tan_1( b/a)1-3) cos2 x + sin 2 x = 11-4) sin 2x 2 sin x cos x1-5) cos 2x = cos2 x sin 2 x 2 cos2 x 1 = 1 2 sin2 x1-6) cos x cos y = \ cos(:r + y) + \ cos(x y)1-7) s in x sin y | cos(x y) | cos(:r + y)1-8) sin x cos y \ sin(x + y) + \ sin(x y)1-9) cos(x y) cos x cos y =f sin x sin y1-10) sin (x y) sin x cos y cos x sin y

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480 APPENDIX A

(1-11) cos2 x + cos2(x - 7r) + cos2(x H- 7r) = (1-12) sin2 x + sin2(x - |TT) + sin2(x + |TT) = |(1-13) sinx cosx + sin(x |7r) COS(X |7r) + sin(x + |7r) COS(X + | ) = 0(1-14) cosx + cos(x |7r) + cos(x + |7r) = 0(1-15) sin x + sin(x |7r) + sin(x + |7r) = 0(1-16) sin x cos y + sin(x |7r) cos(y 7r) + sin(x + |7r) cos(y + |7r)

- | sin(x - y)(1-17) si n x sin y + sin(x |7r) sin(y |7r) + sin(x + |7r) sin(y + |7r)

= | cos(x y)(1-18) cos x sin y + cos(x |7r) sin(y |7r) + cos(x + |7r) sin(y + |7r)

= - f s in (x -y )(1-19) COS X COS 7/ + COs(x |7r) COs(y 7r) + COs(x + |7r) COs(y + |7r)

= | cos(x y)(1-20) sin x cos y + sin(x + |7r) cos(y |7r) + sin(x |7r) cos(y + 7r)

= | sin(x + y)(1-21) sin x s i n y + sin(x + |7r) sin(y |7r) + sin(x |7r) sin(y + 7r)

= - c o s ( x + y)(1-22) cos x sin y + cos(x + |7r) sin(y |7r) + cos(x |7r) sin(y + |7r)

= | sin(x + y)(1-23) co sx co sy + cos(x + |7r) cos(y |7r) + cos(x |7r) cos(y + |7r)

= | cos(x + y)