BNG-202 Biomechanics II Equation Sheet + Particle Kinematics v = ds dt a = dv dt ads = vdv v x =(v i ) x x = x i +(v i ) x t v y =(v i ) y - gt y = y i +(v i ) y t - 1 2 gt 2 v 2 y =(v i ) 2 y - 2g(y f - y i ) ⌃ v =˙ s ˆ u t = v ˆ u t ⌃ a =˙ v ˆ u t + v 2 ρ ˆ u n ρ = [1 + ( dy dx ) 2 ] (3/2) | d 2 y dx 2 | ⇥ v A/B = ⇥ v A - ⇥ v B ~ r A/B = ~ r A - ~ r B ~ v =˙ r ˆ u r + r ˙ ✓ ˆ u ✓ +˙ z ˆ u z ~ a = (¨ r - r ˙ ✓ 2 )ˆ u r +(r ¨ ✓ +2˙ r ˙ ✓)ˆ u ✓ +¨ z ˆ u z ⇡rad = 180degrees Particle Kinetics: Force and Acceleration ⌃F x = ma x ⌃F y = ma y ⌃F z = ma z tanθ = dy dx ⌃F n = ma n ⌃F t = ma t ⌃F b =0 tan ⇥ = r dr/dθ ⌃F r = ma r ⌃F ✓ = ma ✓ ⌃F z = ma z f = μ k N F = ks Particle Kinetics: Work and Energy T 1 + V 1 + ⌃U 12 = T 2 + V 2 T = 1 2 mv 2 V g = ±Wy = ±mgh V e = 1 2 ks 2 U 12 = Z 2 1 F ds ⌃mv 1 = ⌃mv 2 e = [(v B ) 2 - (v A ) 2 ] [(v A ) 1 - (v B ) 1 ] Particle Kinetics: Impulse and Momentum m ⌃ v 1 + ⇥ ⌃ F dt = m ⌃ v 2 Line of Impact (LI) Plane of Contact (PC) (v A PC ) 1 =(v A PC ) 2 (v B PC ) 1 =(v B PC ) 2 ⌃m(v LI ) 1 = ⌃m(v LI ) 2 e = [(v B LI ) 2 - (v A LI ) 2 ] [(v A LI ) 1 - (v B LI ) 1 ] * * * These are equations you use for object hitting a wall, ground, table top etc.