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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 ω 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 Ω . 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 ω = | ω | as a function of L , r , Ω = | Ω | , and angle β . (c) Compute the absolute angular-momentum vector relative to Gear A’s center of mass, H G , as a function of m , L , r , Ω and β . (d) Compute ˙ H G , the absolute rate of change of H G , as a function of m , L , r , Ω and β ....
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- Angular Momentum, ... ..., Coordinate system, 2L