A custom-fabricated component for a machine consists of a steel (y = 0.28 lbf/in?), 5-in diameter rod and a thin-walled bronze (y = 0.3 lbf/in³) bushing that are both 3.6 in long. For clarity, the central piece with the hole pattern is made of steel and that steel piece is surrounded by the bronze bushing. Determine the mass moment of inertia of the component about an axis parallel to its length and passing through point O (located at the outer surface of the bushing). All dimensions are in inches.
A custom-fabricated component for a machine consists of a steel (y = 0.28 lbf/in?), 5-in diameter rod and a thin-walled bronze (y = 0.3 lbf/in³) bushing that are both 3.6 in long. For clarity, the central piece with the hole pattern is made of steel and that steel piece is surrounded by the bronze bushing. Determine the mass moment of inertia of the component about an axis parallel to its length and passing through point O (located at the outer surface of the bushing). All dimensions are in inches.
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Transcribed Image Text:A custom-fabricated component for a machine consists of a steel (y = 0.28 lbf/in?), 5-in diameter rod and a thin-walled bronze (y =
0.3 lbf/in³) bushing that are both 3.6 in long. For clarity, the central piece with the hole pattern is made of steel and that steel piece
is surrounded by the bronze bushing. Determine the mass moment of inertia of the component about an axis parallel to its length
and passing through point O (located at the outer surface of the bushing). All dimensions are in inches.
Expert Solution
Step 1
The mass of the solid steel cylinder without any hole pattern is
The mass of the bronze part is
The mass of the hole pattern is
Step 2
The mass moment of inertia of the solid steel part can be determined as shown below.
The mean radius of the bronze part is
The moment of inertia of the bronze part can be determined as,
The moment of inertia of the hole pattern about the centroidal axis is
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