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Unformatted text preview: 336 CHAPTER 8. RIGID-BODY KINETICS 8.7 Chapter 8, Problem 7 Problem: Gear A of mass m and radius r is constrained to roll on fixed Gear B. It rotates with counterclockwise angular velocity about Axle AD, which has negligible mass and length L . Axle AD is connected by a clevis to vertical Shaft DE, which rotates counterclockwise with constant angular velocity . You can ignore effects of friction. HINT: This problem is most conveniently solved in a coordinate system ( x I y I z I ) in which z I is aligned with Axle AD. Gear A can be represented as a thin disk. In its principal axis system, the inertia tensor is [ I ] = 1 4 mr 2 1 4 mr 2 1 2 mr 2 (a) The two gears make contact at Point C. Why is the absolute velocity of Point C zero? (b) Determine = | | as a function of L , r , = | | , and angle . (c) Compute the absolute angular-momentum vector relative to Gear As center of mass, H G , as a function of m , L , r , and . (d) Compute H G , the absolute rate of change of H G , as a function of m , L , r , and ....
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