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Unformatted text preview: 1 ME 242 Dynamics February 2, 2009 Eric Wang Todays Key Concepts 2D Kinematics Path Coordinate 1D motion along a curve Path Coordinates The coordinate system moves with the car Tangential direction Normal direction e t e n e t Example: unicycle e n Center of Curvature & Radius of Curvature At any instant in time any curve can be approximated as a circular arc Normal Direction The normal unit vector always points towards the center of curvature 2 Velocity If radius is constant v p = ve t v p = r e r + r e r = r = v e t e e n e r Acceleration If radius is constant, then only have centripetal & tangential components Polar vs. Path a P = ( r r 2 ) e r + (2 r + r ) e r P / O = re r v p = r e r + r e No equivalent v p = ve t a P = v e t + v 2 r c e n Given: Ferris wheel has 30ft radius Magnitude of acceleration of P is 0.33 ft/s 2 Constant speed ride Find: Rotational speed Solution:...
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- Spring '06