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Unformatted text preview: 8.4. CHAPTER 8, PROBLEM 4 325 8.4 Chapter 8, Problem 4 Problem: A right-circular cone of mass m , height h and base radius r spins about its axis of symmetry with angular velocity ω . Simultaneously, the entire cone revolves about the x axis with angular velocity Ω . (a) Appealing to tabulated values, state the moment of inertia tensor for the center-of-mass based principal axis system and the location of the cone’s center of mass. (b) Determine the moment of inertia tensor relative to the tip of the cone. (c) Determine the angular-momentum vector relative to the tip of the cone, H O . (d) Determine d H O /dt . (e) If the net moment about the x axis is M O = − m Ω 2 r 2 j , what is ω ? Solution: (a) From tabulated values, the center of mass of the cone is located at r = 3 4 h k The moment of inertia tensor for the center-of-mass based principal axis system is [ I I ] = ⎡ ⎣ 3 20 m D r 2 + 4 h 2 i 3 20 m D r 2 + 4 h 2 i 3 10 mr 2 ⎤ ⎦ (b) Using the Parallel-Axis Theorem, the components of the moment of inertia tensor relative to the tip of...
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This note was uploaded on 12/16/2010 for the course AME 301 at USC.