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Document Title
Fundamentals of Stress and Vibration Chapter Title
[A Practical guide for aspiring Designers / Analysts] 2. Engineering Mechanics
[Total MMOI = MMOI of the elemental section about the axis of rotation (treating it as a thin rod) +
MMOI about the vertical diameter of all the elemental sections]
L
L 2
2
2 2 dm ∗ R 2
I
total = πR ρ dx ∗ x + 4 Proved in situation 4
L L
−
−
2 2
L L
2 2
2
2 2 πR ρ dx ∗ R 2
I
total = πR ρ dx ∗ x + 4
L L
−
−
2 2
L L L
2 πR ρ 2 x 3 2 πR ρ L
4
4
2
2
2
I total = πR ρ x dx + dx = πR ρ + x 2
L
4 3 L 4 −
2
− L − L − 2
2 2
L 3 L 3 πR ρ L L πR ρL ∗ L 2 πR ρL ∗ R 2
2
2
4
2
I total = πR ρ + + + = +
24 24 4 2 2 12 4
mL 2 mR 2
= I total = +
12 4
Situation 6: find the mass moment of inertia for a sphere, shown in [Fig 2.33]
[Fig 2.33: spherical object rotating about its vertical axis]
Page 44 QP No. SSC/Q4401, Version 1.0, NSQF Level 7, Compliant with Aero and Auto Industries,
