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p0808 - 8.8 CHAPTER 8 PROBLEM 8 335 8.8 Chapter 8 Problem 8...

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8.8. CHAPTER 8, PROBLEM 8 335 8.8 Chapter 8, Problem 8 Problem: A projectile of mass m has a radius of gyration R about its axis of symmetry ( x axis) and a radius of gyration 4 R about the transverse axis ( y axis). Its angular velocity, ω , can be resolved into two components. The first is the rate of spin , ω s , which is directed along the axis of symmetry. The second is the rate of precession , ω p , which is parallel to the projectile’s velocity vector (Axis GD). For the projectile shown, the angular-momentum vector relative to its center of mass is H G = H ( i 0 . 032 j ) , where H is a constant. (a) Determine ω as a function of H , m and R . (b) Determine ω s and ω p as functions of H , m , R and the angle θ between the symmetry axis and the velocity vector. HINT: Let ω = ω s i + ω p p ,whe re p is a unit vector parallel to the velocity vector. (c) If the projectile has R =5 cm, m =30 kg, H =0 . 75 kg · m 2 /sec and θ o , compute the projectile’s angular-velocity vector, ω = ω x i + ω y j , and its spin and precession rates, ω s and ω p , respectively.

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p0808 - 8.8 CHAPTER 8 PROBLEM 8 335 8.8 Chapter 8 Problem 8...

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