STATICS. CENTROIDS OF MASSES, AREAS, LENGTHS, AND VOLUMES The following formulas are for discrete masses, areas, lengths, and volumes: r c

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STTS FORE foe is veto qutit. t is defied we its () mgitude, () oit of litio, d () dietio e kow. Te veto fom of foe is F F i F j RESULTNT (TWO DMENSONS) Te esultt, F, of foes wit omoets F,i d F,i s te mgitude of i, i, i i F > d! F d! F H Te esultt dietio wit eset to te -is is i i, i i, i t e! F! F RESOLUTON OF FORE F F os ; F F os ; F z F os z os F /F; os F /F; os z F z /F Setig foe ito omoets we te geomet of foe is kow d R z F (/R)F; F (/R)F; F z (z/r)f MOMENTS (OUPLES) sstem of two foes tt e equl i mgitude, oosite i dietio, d llel to e ote is lled oule. momet M is defied s te oss odut of te dius veto d te foe F fom oit to te lie of tio of te foe. M F; M F z zf, M zf F z, d M z F F. o ENTRODS OF MSSES, RES, LENGTHS, ND VOLUMES Te followig fomuls e fo disete msses, es, legts, d volumes: Σ m /Σ m, wee m te mss of e tile mkig u te sstem, te dius veto to e tile fom seleted efeee oit, d te dius veto to te etoid of te totl mss fom te seleted efeee oit. Te momet of e (M ) is defied s M Σ M Σ Te etoid of e is defied s M / Σ / M / Σ / wee Σ MOMENT OF NERT Te momet of ieti, o te seod momet of e, is defied s d d Te ol momet of ieti J of e out oit is equl to te sum of te momets of ieti of te e out two eediul es i te e d ssig toug te sme oit. z J ( ) d, wee te dius of gtio (s defied o te et ge) SYSTEMS OF FORES F Σ F M Σ ( F ) Equiliium Requiemets Σ F Σ M STTS

Momet of eti Pllel is Teoem Te momet of ieti of e out is is defied s te momet of ieti of te e out llel etoidl is lus tem equl to te e multilied te sque of te eediul diste d fom te etoidl is to te is i questio. l d l d,wee d, d diste etwee te two es i questio,, te momet of ieti out te etoidl is, d l, l te momet of ieti out te ew is. Rdius of Gtio Te dius of gtio,, is te diste fom efeee is t wi ll of te e e osideed to e oetted to odue te momet of ieti. ; ; J Podut of eti Te odut of ieti (, et.) is defied s: d, wit eset to te -oodite sstem, Te llel-is teoem lso lies: ' d d fo te -oodite sstem, et. wee d -is diste etwee te two es i questio, d d -is diste etwee te two es i questio. BELT FRTON F F e µ, wee F foe eig lied i te dietio of imedig motio, F foe lied to esist imedig motio, µ oeffiiet of stti fitio, d te totl gle of ott etwee te sufes eessed i dis. STTLLY DETERMNTE TRUSS Ple Tuss: Metod of Joits Te metod osists of solvig fo te foes i te memes witig te two equiliium equtios fo e joit of te tuss. Σ F d Σ F, wee F oizotl foes d meme omoets d F vetil foes d meme omoets. Ple Tuss: Metod of Setios Te metod osists of dwig fee-od digm of otio of te tuss i su w tt te ukow tuss meme foe is eosed s etel foe. ONURRENT FORES ouet-foe sstem is oe i wi te lies of tio of te lied foes ll meet t oe oit. two-foe od i stti equiliium s two lied foes tt e equl i mgitude, oosite i dietio, d ollie. FRTON Te lgest fitiol foe is lled te limitig fitio. fute iese i lied foes will use motio. F µ s N, wee F fitio foe, µ s oeffiiet of stti fitio, d N oml foe etwee sufes i ott. SREW THRED Fo sew-jk, sque ted, M P t (α ± φ), wee is fo sew tigteig, is fo sew looseig, M etel momet lied to is of sew, P lod o jk lied log d o te lie of te is, te me ted dius, α te it gle of te ted, d µ t φ te oite oeffiiet of fitio. STTS

Figue e & etoid e Momet of eti (Rdius of Gtio) Podut of eti STTS / / / / / / / ( )/ / / / ( ) ( ) ( ) si ( os )/ ( si )/ / / / / / / / / [ ( )] [ ( )] [ ( )] J ( ) ( ) ( ) 7 ( ) ( ) ( ) ( ) ( ) [ si( os ) ] ( si ) [ si( os) ] ( sios) ( ) ( ) ( ) si si ( os ) ( si) ( os) ( os) House, Geoge W., d Dold E. Hudso, lied Meis Dmis, D. V Nostd om,., Pieto, NJ, 99. Tle eited emissio of G.W. House & D.E. Hudso. ( ) [ ( ) ] ( ) 7 ( si os) 7

STTS J ( ) J / /() 7 9 9 si ( si os )/ ( si os )/ os si os si os si si si os si os si os si os si os si os si os si os si House, Geoge W., d Dold E. Hudso, lied Meis Dmis, D. V Nostd om,., Pieto, NJ, 99. Tle eited emissio of G.W. House & D.E. Hudso. Figue e & etoid e Momet of eti (Rdius of Gtio) Podut of eti

7 STTS / / 7 7 7 7 / / / / /7 7 / House, Geoge W., d Dold E. Hudso, lied Meis Dmis, D. V Nostd om,., Pieto, NJ, 99. Tle eited emissio of G.W. House & D.E. Hudso. (/ ) (/ / ) / Figue e & etoid e Momet of eti (Rdius of Gtio) Podut of eti

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