p0276 - v = f τ e r t τ e θ The acceleration vector is a...

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190 CHAPTER 2. PARTICLE KINEMATICS 2.76 Chapter 2, Problem 76 Problem: The position of a particle in two-dimensional cylindrical coordinates is given by r = f t/ τ and θ = t/ τ ,whe re t is time, f is a constant length scale and τ is a constant time scale. Determine the velocity and acceleration vectors in terms of f , τ and θ . Solution: First, differentiation of the particle’s coordinates yields ˙ r = f τ , ¨ r =0 , ˙ θ = 1 τ , ¨ θ =0 Thus, the velocity vector is v = ˙ r e r + r ˙ θ e θ = f τ e r + f t τ 1 τ e θ = f τ e r + f t τ 2 e θ
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Unformatted text preview: v = f τ } e r + t τ e θ ] The acceleration vector is a = p ¨ r − r ˙ θ 2 Q e r + p r ¨ θ + 2 ˙ r ˙ θ Q e θ = w − f t τ 1 τ 2 W e r + w 0 + 2 f τ 1 τ W e θ = − f t τ 3 e r + 2 f τ 2 e θ Rearranging terms, we find a = f τ 2 } − t τ e r + 2 e θ ] Finally, since θ = t/ τ , we can rewrite the velocity and acceleration vectors as follows. v = f τ [ e r + θ e θ ] a = f τ 2 [ − θ e r + 2 e θ ]...
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This note was uploaded on 05/11/2011 for the course AME 301 taught by Professor Shiflett during the Spring '06 term at USC.

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