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chapter6-a-student_0-3

# chapter6-a-student_0-3 - MEEG439 MEEG439 SPRING2006 Chapter...

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MEEG439 MEEG439 SPRING2006 Chapter 6 Velocity Analysis 6.0 Introduction Use position and velocity analysis as stepping stones to acceleration (and hence force) analysis We can use velocities to look at energies and power losses in a system Note: we won’t be covering the graphical velocity analysis techniques in any depth Also, we won’t be using the complex number approach for velocity and acceleration analysis 6.1 Definition of Velocity Velocity is the rate of change of position with respect to time Velocity is a vector quantity Angular velocity for 2-D can be considered a scalar quantity (even though it is really a vector about the z axis) , d d dt dt θ ϖ θ = = = = r v r & & Given a position vector (cos sin ) a b θ θ = + r i j ( sin cos ) a ϖ θ θ = - + r i j & Note that for this case (rotation about a fixed point) the velocity vector is perpendicular to the position vector θ r r . Recall our position equation or P A PA PA P A = + = - r r r r r r Differentiating with respect to time or P A PA PA P A = + = - v v v v v v Now, if points P and A are on the same body, v PA is the velocity difference If P and A are on different bodies, v PA is the relative velocity I will tend to call both of these relative velocity 6.2 Graphical Velocity Analysis Before calculators, had to solve such problems graphically

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