ME 242 Lecture 7 02.04 - ME 242 Dynamics February 4 2009 Today's Key Concepts Relative motion Relative position Relative velocity Relative acceleration

# ME 242 Lecture 7 02.04 - ME 242 Dynamics February 4 2009...

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1 ME 242 Dynamics February 4, 2009 Eric Wang Today’s Key Concepts Relative motion Relative position Relative velocity Relative acceleration Degrees of Freedom • Constraints Relative Position r A / O = r B / O + r A / B Velocities d dt XYZ r A / O = r B / O + r A / B ( ) d dt XYZ r A / O = d dt XYZ r B / O + d dt XYZ r A / B r A / O = r B / O + r A / B Absolute Velocities d dt XYZ r A / O = d dt XYZ r B / O + d dt XYZ r A / B d dt XYZ r A / O = v A / O = v A d dt XYZ r B / O = v B / O = v B Which Train is Moving?
2 Relative Velocity Imagine: 1. A & B moving at same velocity 2. A moving towards stationary B 3. B moving towards stationary A d dt XYZ r A / B = v A / B Accelerations r A / O = r B / O + r A / B v A = v B + v A / B a A = a B + a A / B Common Mistake r A / O = r B / O + r A / B r A / O = r B / O + r B / A Learn the nomenclature & draw the picture instead of memorizing the formula! Flipping it around r A / O = r B / O + r A / B r B / O = r A / O + r B / A r A / B = r B / A Same for velocity & acceleration r A / B = r B / A v A / B = v B / A a A / B = a B / A Example (prob. 2.5.3) Given: Speed of A = 44 ft/s (constant)