p0276 - v = f } e r + t e ] 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 } e r + t e ] The acceleration vector is a = p r r 2 Q e r + p r + 2 r Q e = w f t 1 2 W e r + w 0 + 2 f 1 W e = f t 3 e r + 2 f 2 e Rearranging terms, we find a = f 2 } t e r + 2 e ] Finally, since = t/ , we can rewrite the velocity and acceleration vectors as follows. v = f [ e r + e ] a = f 2 [ e r + 2 e ]...
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