Ho010Fb26e6G_1210016259_jwk572

Ho010Fb26e6G_1210016259_jwk572 - midterm 02 – KIM JI –...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: midterm 02 – KIM, JI – Due: Oct 17 2007, 7:00 pm 1 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 a c 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 sin 2 θ = 2 sin θ cos θ, cos 2 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 dθ sin θ = cos θ , d dθ cos θ = − sin θ , d dx const = 0 Measurements Dimensional analysis: e.g. , F = ma → [ M ][ L ][ T ] − 2 , or F = m v 2 r → [ M ][ L ][ T ] − 2 Summation: ∑ N i =1 ( ax i + b ) = a ∑ N i =1 x i + bN Motion One dimensional motion: v = d s dt , a = d v dt Average values: ¯ v = s f − s i t f − t i , ¯ a = v f − v i t f − t i One dimensional motion (constant acceleration): v ( t ) : v = v + at s ( t ) : s = ¯ v t = v t + 1 2 at 2 , ¯ v = v + v 2 v ( s ) : v 2 = v 2 + 2 as Nonuniform acceleration: x = x + v t + 1 2 at 2 + 1 6 j t 3 + 1 24 st 4 + 1 120 k t 5 + 1 720 pt 6 + ... , (jerk, snap, ... ) Projectile motion: t rise = t fall = t trip 2 = v y g h = 1 2 g t 2 fall , R = v ox t trip Circular: a c = v 2 r , v = 2 π r T , f = 1 T (Hertz=s − 1 ) Curvilinear motion: a = radicalBig a 2 t + a 2 r Relative velocity: vectorv = vectorv ′ + vectoru Law of Motion and applications Force: vector F = mvectora, F g = mg, vector F 12 = − vector F 21 Circular motion: a c = v 2 r , v = 2 π r T = 2 π r f Friction: F static ≤ μ s N F kinetic = μ k N Equilibrium (concurrent forces): ∑ i vector F i = 0 Energy Work (for all F): Δ W = W AB = W B − W A F bardbl s = Fs cos θ = vector F · vectors → integraltext B A vector F · dvectors (in Joules) Effects due to work done: vector F ext = mvectora − vector F c − vector f nc W ext | A → B = K B − K A + U B − U A + W diss | A → B Kinetic energy: K B − K A = integraltext B A mvectora · dvectors , K = 1 2 mv 2 K (conservative vector F ): U B − U A = − integraltext B A vector F · dvectors U gravity = mg y , U spring = 1 2 k x 2 From U to vector F : F x = − ∂ U ∂x , F y = − ∂ U ∂y , F z = − ∂ U ∂z F gravity...
View Full Document

This note was uploaded on 05/05/2008 for the course PHY 303K taught by Professor Turner during the Fall '08 term at University of Texas.

Page1 / 13

Ho010Fb26e6G_1210016259_jwk572 - midterm 02 – KIM JI –...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online