Dynamics Crib Sheet2

Dynamics Crib Sheet2 - ∑ ∑ = 2 1 i i i i v m v m...

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RECTILINEAR KINEMATICS (straight line motion of particles) RECTILINEAR KINEMATICS (constant acceleration) PROJECTILE MOTION (same as Rectilinear Kinematics above, but ) FRICTION Slip, F =µ s N No Slip, F < µ s N WORK ENERGY = + - 2 2 1 1 T U T U Force = Fcosθ * distance U Force = ds F S S 2 1 cos θ U weight = +/-mg(h 2 -h 1 ) U spring = -(1/2)k ) ( 2 1 2 2 s s - U constant couple = m (Δθ If m is not constant, U couple = d m 2 1 T = 2 2 2 1 2 1 ϖ G G I mv + POWER P = dU/dt dU=Fcosθds = F dot dr P = F dot v Parametric Equations Given: can be R (t), v (t), or a (t) n-t acceleration or and RELATIVE VELOCITY (r = position…to get velocity or acceleration, just take the derivative of the respective prior one) r B = r A + r B/A v B/A = x r B/A Instantaneous Center (IC) Method : v B = v B/IC v B/IC = x r B/IC RIGID BODY MOTION and FIXED AXIS ROTATION Angular motion Constant α Fixed Axis Rotation – motion of a POINT r v = MESHED GEARS ω=dθ/dt α=dω/dt Arc Lengths Velocities Tangential accelerations CONSERVATION OF LINEAR MOMENTIUM : When the sum of external impulses is zero
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Unformatted text preview: ∑ ∑ = 2 1 ) ( ) ( i i i i v m v m Kinetic Equations of Motion ∑ = X G X ma F ∑ = Gy Y ma F 2 G G mk I = m I k G G = 2 md I I G axis + = ⋅ = ∑ G G I M ∑ ∑ = P K P M M ) ( Kinetic Moment. When translating (no rotation) α=0 but the Kinetic Moment is not zero ⋅ = ∑ G Pin I M Fixed axis rotation only. When G is the fixed axis , a G = 0. dt ds v = dt dv a = vdv ads = at v v + = 2 2 1 t a t v s s + + = ) ( 2 2 2 s s a v v-+ = g a a y x-= = j t g i t f t R ˆ ) ( ˆ ) ( ) ( + = n n t t a a u u a + = dt dv a vdv ds a t t / = = ρ 2 v a n = dt d = dt d = d d = ( 29 2 2 2 2 2-+ = + + = + = c c c t t t r s = r a t = r v n r a 2 2 = = B B A A r r = B B A A B A r r v v = ⇒ = B B A A t B t A r r a a = ⇒ =...
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