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p0802

# p0802 - 322 CHAPTER 8 RIGID-BODY KINETICS 8.2 Chapter 8...

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322 CHAPTER 8. RIGID-BODY KINETICS 8.2 Chapter 8, Problem 2 Problem: A space probe of mass M is struck at Point A by a meteorite of mass m and initial velocity v o = V ( 3 4 i 15 16 j + k ) . Point A is located at r A =6 R i + 1 2 R k . The coordinate axes shown are the principal centroidal axes of inertia. The radii of gyration for the three principal axes are k x = 9 8 R , k y = 5 4 R and k z = R . After passing through the probe’s solar panel, the meteorite’s speed is 80% of its initial value and its direction is unchanged. Determine the angular velocity of the probe after the meteorite strike. Express your answer in terms of m , M , V and R . Solution: The position vector from the space probe’s center of mass to the point at which the meteorite strikes the probe is r A R i + 1 2 R k Thus, the meteorite’s linear- and angular-momentum vectors just before the strike are m v o = mV w 3 4 i 15 16 j + k W = 1 16 mV (12 i 15 j +16 k ) r A × m v o = e e e e e e ij k 6 R 0 1 2 R 3 4 mV 15 16 mV mV e e e e e e = 15 32 mV R ( i 12 j 12 k )

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p0802 - 322 CHAPTER 8 RIGID-BODY KINETICS 8.2 Chapter 8...

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