{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

172_Problem CHAPTER 9

# 172_Problem CHAPTER 9 - PROBLEM 9.135 The cups and the arms...

This preview shows page 1. Sign up to view the full content.

PROBLEM 9.135 The cups and the arms of an anemometer are fabricated from a material of density ρ . Knowing that the moment of inertia of a thin, hemispherical shell of mass m and thickness t with respect to its centroidal axis , GG is 5 ma 2 /12, determine ( a ) the moment of inertia of the anemometer with respect to the axis , AA ( b ) the ratio of a to l for which the centroidal moment of inertia of the cups is equal to 1 percent of the moment of inertia of the cups with respect to the axis . AA SOLUTION ( a ) First note 2 arm arm 4 m V d l π ρ ρ = = × and cup cup dm dV ρ = ( )( )( ) 2 cos a t ad ρ π θ θ = Then 2 2 cup cup 0 2 cos m dm a t d π πρ θ θ = ∫ = ∫ [ ] 2 2 0 2 sin a t π πρ θ = 2 2 a t πρ = Now ( ) ( ) ( ) anem. cups arms AA AA AA I I I = + Using the parallel-axis theorem and assuming the arms are slender rods, have
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}