96_Dynamics 11ed Manual - Engineering Mechanics - Dynamics...

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Engineering Mechanics - Dynamics Chapter 12 and z = dt 2 . Determine the unit vector that specifies the direction of the binormal axis to the osculating plane with respect to a set of fixed x, y, z coordinate axes when t = t 1 . Hint: Formulate the particle’s velocity v p and acceleration a p in terms of their i , j , k components. Note that xr cos θ () = and yr sin = . The binormal is parallel to v p × a p . Why? Given: b 8f t = c 4 rad s = d 6 ft s 2 = t 1 2s = Solution: r p1 b cos ct 1 b sin 1 dt 1 2 = v p1 b c sin 1 bc cos 1 2 1 = a p1 b c 2 cos 1 b c 2 sin 1 2 d = Since v p and a p are in the normal plane and the binormal direction is perpendicular to this plane then we can use the cross product to define the binormal direction. u v p1 a p1 × v p1 a p1 × = u 0.581
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