ME 242 Lecture 5 1.30

ME 242 Lecture 5 1.30 - 1 ME 242 Dynamics Eric Wang...

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Unformatted text preview: 1 ME 242 Dynamics January 30, 2009 Eric Wang Today’s Key Concepts 2D Kinematics • Polar Coordinate • Cylindrical Coordinates Cartesian vs. Polar r P / O = xi + y j r P / O = re r e θ e r θ cos θ 1 cos θ-sin θ sin θ e θ j i e r k k Coordinate Transformation Array j i Velocity v P = d dt XYZ r P / O = dr dt e r + r d dt XYZ e r = ˙ r e r + r d dt XYZ cos θ i + sin θ j r P / O = re r = ˙ r e r + r ˙ θ − sin θ i + cos θ j ( ) = ˙ r e r + r ˙ θ e θ Eqn 2.52 in text cos θ cos θ-sin θ sin θ e θ j i e r Given: • Car driving towards O at constant speed v Find: magnitude of the derivative ˙ r B / A (scalar derivative) θ = 63.4 2 Solution: • Velocity of B in Cartesian coordinates: v B = − v (cos45 i + sin45 j ) v B = − v 2 2 ( i + j ) v B = v x i + v y j = ˙ r e r + r ˙ θ e θ • Velocity of B is the same in all coordinates systems!...
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This note was uploaded on 09/19/2009 for the course ME 242 taught by Professor Kam during the Spring '06 term at Nevada.

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ME 242 Lecture 5 1.30 - 1 ME 242 Dynamics Eric Wang...

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