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Unformatted text preview: 1 ME 242 Dynamics February 2, 2009 Eric Wang Today’s 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 ˙ θ e θ r ˙ θ = r ω = v e t e θ − e n e r Acceleration • If radius is constant, then only have centripetal & tangential components Polar vs. Path a P = (˙ ˙ r − r ˙ θ 2 ) e r + (2˙ r ˙ θ + r ˙ ˙ θ ) e θ r P / O = re r v p = ˙ r e r + r ˙ θ e θ 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
- Acceleration, Velocity, Radius of curvature, Center of Curvature & Radius of Curvature