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Formulae_Mech_page1

# Formulae_Mech_page1 - Mechanics Basic Physical Concepts 3...

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Mechanics - Basic Physical Concepts Math: Circle: 2 π r , π r 2 ; Sphere: 4 π r 2 , (4 / 3) π r 3 Quadratic Eq.: ax 2 + bx + c = 0, x = b ± b 2 4 ac 2 a Cartesian and polar coordinates: x = r cos θ, y = r sin θ , r 2 = x 2 + y 2 , tan θ = y x Trigonometry: cos α cos β + sin α sin β = cos( α - β ) sin α + sin β = 2 sin α + β 2 cos α β 2 cos α + cos β = 2 cos α + β 2 cos α β 2 sin2 θ = 2 sin θ cos θ, cos2 θ = cos 2 θ - sin 2 θ 1 - cos θ = 2 sin 2 θ 2 , 1 + cos θ = 2 cos 2 θ 2 Vector algebra: vector A = ( A x ,A y ) = A x ˆ ı + A y ˆ Resultant: vector R = vector A + vector B = ( A x + B x ,A y + B y ) Dot: vector A · vector B = AB cos θ = A x B x + A y B y + A z B z Cross product: ˆ ı × ˆ = ˆ k , ˆ × ˆ k = ˆ ı , ˆ k × ˆ ı = ˆ vector C = vector A × vector B = vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle ˆ ı ˆ ˆ k A x A y A z B x B y B z vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle C = AB sin θ = A B = AB , use right hand rule Calculus: d dx x n = nx n 1 , d dx ln x = 1 x , d sin θ = cos θ , d cos θ = -
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