COSMOS Chapter 9 Solution 178 - Edubirdie

University:
Michigan State University
Course:
ERG 160 | Success in Science, Technology, Engineering, and Mathematics
Academic year:

2020
Views:

378

Pages:

1
Author:

Sean Horton

COSMOS: Complete Online Solutions Manual Organization System Chapter 9, Solution 178. I y + Iz ≥ Ix (i) To prove By ( 2 2 ) I y = ∫ z + x dm Then ( ) ( ) I z = ∫ x + y dm ( ) I y + I z = ∫ z 2 + x 2 dm + ∫ x 2 + y 2 dm ( ) = ∫ y 2 + z 2 dm + 2∫ x dm Now.. 2 2 ∫ ( y + z ) dm = I x and ∴ I y + Iz ≥ Ix Q.E.D. 2 ∫ x dm ≥ 0 The proofs of the other two inequalities follow similar steps. (ii) If the x axis is the axis of revolution, then I y = Iz and from part (i) I y + I z ≥ I x or 2I y ≥ I x or I y ≥ 1 Ix 2 Q.E.D. definition

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