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Document Title
Fundamentals of Stress and Vibration 2. Engineering Mechanics Chapter
[A Practical guide for aspiring Designers / Analysts]

– ‹• –‘ „‡ ‘–‡† –Šƒ–ǡ –Š‡ ‘ ‡’– ‘ˆ ƒ”‡ƒ ‘‡– ‘ˆ ‹‡”–‹ƒ ȋ Ȍ ȋ–‘ „‡ ‹–”‘†— ‡† ‹ ‘Ž‹†
‡ Šƒ‹ •Ȍǡ •Š‘—Ž† ‘– „‡ ‘ˆ—•‡† ™‹–Š ƒ•• ‘‡– ‘ˆ ‹‡”–‹ƒǡ ƒ•ǡ ‹• ƒ ’”‘’‡”–› ‘ˆ –Š‡
ƒ••ǡ ™Š‡”‡ƒ•ǡ ‹• ƒ ’”‘’‡”–› ‘ˆ –Š‡ ”‘••-•‡ –‹‘ƒŽ ‰‡‘‡–”›Ǥ

—”–Š‡”ǡ –Š‡ ƒ•• ‘‡– ‘ˆ ‹‡”–‹ƒ ‹• –Š‡ ”‡•‹•–ƒ ‡ ‘ˆˆ‡”‡† ƒ‰ƒ‹•– ƒ‰—Žƒ” ”‘–ƒ–‹‘• ƒ† ƒ”‡ƒ
‘‡– ‘ˆ ‹‡”–‹ƒ ‹• –Š‡ ”‡•‹•–ƒ ‡ ‘ˆˆ‡”‡† ƒ‰ƒ‹•– ƒ‰—Žƒ” †‡ˆ‘”ƒ–‹‘•Ǥ
Š‡ ‹• ˆ‘—† ˆ‘” ˜ƒ”‹‘—• –›’‡• ‘ˆ •Šƒ’‡• ƒ„‘—– ƒ ‰‹˜‡ ƒš‹• ‘ˆ ”‘–ƒ–‹‘Ǥ ȏ ‘” ‡šƒ’Ž‡ǡ ƒ
”‘–ƒ–‹‰ •Šƒˆ–ǡ ™‹–Š ƒ †‹• ‘—–‡† ‘ ‹–ǡ ‹• ‡“—‹˜ƒŽ‡– –‘ ƒ ”‘† ™‹–Š ƒ ›Ž‹†‡”ȐǤ Š‡”‡ˆ‘”‡ǡ ˆ‘”
ƒ› ‘’‘‡–•Ȁ‰‡‘‡–”‹‡•ǡ –Š‡ ‹• ˆ‘—† ƒ• ˆ‘ŽŽ‘™•ǣ
‹–—ƒ–‹‘ ͳǣ ‘•‹†‡” ƒ ”‘† ƒ ‡Ž‡”ƒ–‡† ƒ„‘—– ƒ ƒš‹• –Š”‘—‰Š ‘‡ ‘ˆ ‹–• ‡†• ƒ• •Š‘™ ‹ ȏ ‹‰
ʹǤʹ͹ȐǤ Š‡ ”‘† ‹• ’”‹•ƒ–‹ ƒ† —‹ˆ‘”Ǥ ‡– —• ‘’—–‡ –Š‡ ˆ‘” –Š‹• •‹–—ƒ–‹‘Ǥ

[Fig 2.27: Rod accelerating about one of its ends]

Solution 1: here, we could utilize the formula derived for a general case as shown in [Fig 2.26].

L L L
m m x 3 mL 2
2
2
I = dmx = dx x = =
L L 3 3
0 0 0
Situation 2: consider a rod accelerated about an axis passing through its CG as shown in
[Fig 2.28]. The rod is prismatic and uniform. Let us compute the MMOI for this situation.

[Fig 2.28: Rod accelerating about its CG]

QP No. SSC/Q4401, Version 1.0, NSQF Level 7, Compliant with Aero and Auto Industries, P
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