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ME 242 Lecture 2 01.23

# ME 242 Lecture 2 01.23 - ME 242 Dynamics Remember Friday...

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1 ME 242 Dynamics January 23, 2009 Remember: Friday class starts at 12:05 Eric Wang Today’s Key Concepts • Vectors • Reference frames • Scalar vs. vector functions • Derivatives of vector functions Vectors • Properties – Magnitude – Direction – Sense (optional) Vectors • Must use a vector symbol • Often have vector and scalar variables with same name V V V r = re r Unit Vectors r = xi + y j x y j i Vector Properties Unchanged r = re r + 0 e θ r e e r

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2 Reference Frames j j i i b 1 b 1 b 2 b 2 Vector Components Scalar vs. Vector Functions • These are scalar functions • These are vector functions b 1 = cos θ i + sin j r = xi + y j x = r cos y = r sin Product Rule (derivatives) dx dt = ˙ x = d dt r cos( ) ( ) = d dt r cos( ) + r d dt cos( ) = ˙ r cos( ) + r d d cos( ) d dt = ˙ r cos( ) r ˙ sin( ) x = r cos Derivatives of vector
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ME 242 Lecture 2 01.23 - ME 242 Dynamics Remember Friday...

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