Formula Formula symbols Units. s = F A. e = x L. E = s ε. k = F δ. G = t γ. e = at. maximum load original cross sectional area. s M E = = N/m.

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Kory Ramsey
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1 A Lit of foulae fo ecanical engineeing pinciple Foula Foula ybol Unit Ste Stain applied foce co ectionalaea cange in lengt oiginal lengt F A e x L Young odulu of elaticity te tain Stiffne foce extenion Modulu of igidity ea te ea tain eal tain coefficient of linea expanion tepeatue ie E ε k F δ G t γ e a N/ eal te in copound ba 1 ( a1 a ) E1 E A ( A E + A E ) 1 1 Ultiate tenile tengt axiu load oiginal co ectional aea Moent foce pependicula ditance M Fd N te ditance fo neutal axi bending oent econd oent of aea Young, odulu adiu of cuvatue M E N/ y I R oque foce pependicula ditance Fd N Powe toque angula velocity P w pn W Hoepowe 1 p 75.7 W oque oent of inetia angula acceleation Ia N ea te toque adiu pola econd oent of aea (igidity)(angle of twit) lengt Aveage velocity ditance tavelled t Gθ L N/ v t / t Fou

2 9 Mecanical Engineeing Pinciple Foula Foula ybol Unit Acceleation cange in velocity a v u / t Linea velocity v w / Angula velocity w t θ pn ad/ Linea acceleation a a / Relationip between initial velocity u, final velocity v, diplaceent, tie t and contant acceleation a Relationip between initial angula velocity w 1, final angula velocity w, angle q, tie t and angula acceleation a Moentu a velocity Ipule applied foce tie cange in oentu v v1 + at 1 ut at + v u + a ω ω1 + a t 1 θ ω1t + a t ω ω1 + aθ / (/) ad/ ad (ad/) kg / kg / Foce a acceleation F a N Weigt a gavitational field W g N Centipetal acceleation a Centipetal foce F Denity a volue v V v / N kg/ Wok done foce ditance oved W F Efficiency Powe ueful output enegy input enegy enegy ued (o wok done) foce velocity P E t Fv W Potential enegy weigt cange in eigt p g t Fou kinetic enegy 1 a (peed) E E k 1 v

3 A Lit of foulae fo ecanical engineeing pinciple 9 Foula Foula ybol Unit kinetic enegy of otation E k 1 Iw 1 oent of inetia (angula velocity) Fictional foce coefficient of fiction noal foce F N N Angle of epoe, q, on an inclined plane tan q Efficiency of cew jack tanθ tan( λ + θ) SHM peiodic tie π diplaceent acceleation π y a π a tiffne π k iple pendulu π L g copound pendulu π G + ( k ) g Foce atio load effot Moveent atio ditance oved by effot ditance oved by load Efficiency foce atio oveent atio Kelvin tepeatue degee Celiu + 7 Quantity of eat enegy a pecific eat capacity cange in tepeatue Q c(t ) New lengt oiginal lengt + expanion L L 1 [1 + a(t )] New uface aea oiginal uface aea + inceae in aea A A 1 [1 + b(t )] New volue oiginal volue + inceae in volue V V 1 [1 + g(t )] Peue foce aea denity gavitational acceleation eigt p F A p g 1 ba 10 5 t Fou

4 9 Mecanical Engineeing Pinciple Foula Foula ybol Unit Abolute peue gauge peue + atopeic peue Metacentic eigt, GM Benoulli equation Coefficient of dicage Caacteitic ga equation GM Px W cot q 1 v1 P + + gz 1 v g z f P + + ( + ) C d C v C c p V p V k pv R Cicula egent In Figue F1, aded aea ( in ) R a a Figue F1 t Fou

5 Suay of tandad eult of te econd oent of aea of egula ection A Lit of foulae fo ecanical engineeing pinciple 95 Sape Poition of axi Second oent of aea, I Radiu of gyation, k Rectangle lengt d beadt b (1) Coinciding wit b () Coinciding wit d () oug centoid, paallel to b () oug centoid, paallel to d bd db bd 1 db 1 d b d 1 b 1 iangle Pependicula eigt bae b (1) Coinciding wit b () oug centoid, paallel to bae () oug vetex, paallel to bae b 1 b 6 b 6 18 Cicle adiu diaete d (1) oug cente pependicula to plane (i.e. pola axi) () Coinciding wit diaete π π π d o π d o 6 () About a tangent 5π o 5π d 6 5 Seicicle adiu Coinciding wit diaete π 8 t Fou

( ) rad ( 2.0 s) = 168 rad

( ) rad ( 2.0 s) = 168 rad .) α 0.450 ω o 0 and ω 8.00 ω αt + ω o o t ω ω o α HO 9 Solution 8.00 0 0.450 7.8 b.) ω ω o + αδθ o Δθ ω 8.00 0 ω o α 0.450 7. o Δθ 7. ev.3 ev π.) ω o.50, α 0.300, Δθ 3.50 ev π 7π ev ω ω o + αδθ o ω ω