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

ʹǤ͸Ǥͳ ƒ•• ‘‡– ‘ˆ ‡”–‹ƒ ȋ Ȍ

‡™–‘ǯ• •‡ ‘† Žƒ™ ‘ˆ ‘–‹‘ ™‡ Šƒ˜‡ ȏ α ƒȐǤ • –Š‡ ƒ’’Ž‹‡† ˆ‘” ‡ Ǯ ǯ ‹ ”‡ƒ•‡•ǡ –Š‡ ‹‡”–‹ƒ Ǯƒǯ
ƒŽ•‘ ‹ ”‡ƒ•‡•Ǥ Š‹• ‹• „‡ ƒ—•‡ǡ ‹‡”–‹ƒ Šƒ• –‘ „‡ ’”‘˜‹†‡† „› –Š‡ ˆ‘” ‡ Ǯ ǯǤ

‹‹Žƒ”Ž›ǡ ™Š‹Ž‡ ”‘–ƒ–‹‰ ƒ „‘†›ǡ –Š‡ ƒ‰—Žƒ” ‹‡”–‹ƒ ȋ‘’’‘•‹–‹‘ –‘ ”‘–ƒ–‹‘Ȍ ‹• ’”‘˜‹†‡† „› –Š‡
ƒ’’Ž‹‡† –‘”“—‡ ǯ ǯǤ

 ƒ•‡ ‘ˆ Ž‹‡ƒ” ‘–‹‘ǡ ƒ•• Ǯǯ ‹• –Š‡ ‹†‡š ‘ˆ ‹‡”–‹ƒǤ ‘™‡˜‡”ǡ ƒ ‡“—‹˜ƒŽ‡– –‡” Šƒ• –‘ „‡
†‡˜‡Ž‘’‡† –‘ ‘’—–‡ –Š‡ ƒ‰—Žƒ” ‹‡”–‹ƒǤ Š‹• –‡” ‹• ƒŽŽ‡† Dzƒ•• ‘‡– ‘ˆ ‹‡”–‹ƒdzǤ

Š‡ ƒ‡ ƒ•• ‘‡– ‘ˆ ‹‡”–‹ƒ ‘”‹‰‹ƒ–‡• ˆ”‘ –Š‡ ˆƒ – –Šƒ–ǡ ‹– ‹• –Š‡ ‘‡– ‘ˆ ƒŽŽ –Š‡ Ž‹‡ƒ”
‹‡”–‹ƒ• ȋƒȌ ‘ˆ –Š‡ ‡Ž‡‡–• –Šƒ– ˆ‘” –Š‡ ”‘–ƒ–‹‰ ‡„‡”Ǥ

‡– —• ‘•‹†‡” ȏ ‹‰ ʹǤʹ͸ȐǤ

[Fig 2.26: Uniform rot rotating with angular acceleration 'α']

[Fig 2.26: Uniform rot rotating with angular acceleration 'α']

Each element on the rod experiences an inertia dmαx . This inertia contributes to a moment about
the ‘z-axis’ as show in [Fig 2.26]. All the elements along the rod contribute to the same sense of
moment. The sum of all the moments is given by:

L
2
Moment of Inertia of the rod = dmαx
0
This inertia has to be provided by the applied torque to sustain the acceleration. Therefore, we have:

L
2
Torque T = dmαx
0
L L
By Newton’s second law of motion: Torque T = dmαx = Iα , by where I = dmx
2
2
0 0
Where (I) is the mass moment of inertia.

Page 38 QP No. SSC/Q4401, Version 1.0, NSQF Level 7, Compliant with Aero and Auto Industries,