Comparison between kinematics in 1D vs circular motion TABLE 4.1 Rotational and linear kinematics for constant acceleration Rotational kinematics Linear kinematics Wf = w; + α Δt Vis + a, At Of = 0; + w; At + ½a(At)² w² = w/² + 2a40 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Vfs = Sf S; + Vis At + 1⁄2a,(At)² = 2 Vfs V₁² = ₁² + 2a, As 2 VisAngular frequency and wave number angular frequency (temporal frequency) w = 2πf= 2TT T D(x, t) = A sin(kx − wt + o) - wave number (spatial frequency) D = 27 λ nam This wave travels at a speed: v=fλ=w/k. XThe principle of superposition The displacement of a medium when more than one wave is present is the sum of the displacements due to each individual wave. 0 0 0 0 1 m/s 1 m/s 2 6 4 Two waves approach 2 2 1 m/s 4 Constructive interference 6 1 m/s Destructive interference t = 0 s 6 4 6 The waves emerge unchanged. 8 8 8 8 x (m) 2 s x (m) 3 s x (m) 4 s x (m)