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140_Problem CHAPTER 9

# 140_Problem CHAPTER 9 - PROBLEM 9.115 The elliptical ring...

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PROBLEM 9.115 The elliptical ring shown was cut from a thin, uniform plate. Denoting the mass of the ring by m , determine its moment of inertia with respect to ( a ) the centroidal axis , BB ( b ) the centroidal axis CC that is perpendicular to the plane of the ring. SOLUTION First note mass m V tA ρ ρ = = = ( )( ) 2 2 t a b ab ρ π = × 3 tab πρ = Also mass area I tI ρ = area 3 m I ab π = ( a ) Using Figure 9.12, ( )( ) 3 3 , area
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