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

mL 2
From . & . , we have: I = - - - - (2.45)
element
12
The total MMOI about the ‘x-axis’ is given by the sum of equations (2.44) and (2.45):

I zz = Rotation of all elements about the z − axis
+ Rotation of all elements about their own axis

mH 2 mL 2
I = +
zz
12 12

ʹǤ͹ ”‹ –‹‘

”‹ –‹‘ ‹• ƒ –”‹„‘Ž‘‰‹ ƒŽ Šƒ”ƒ –‡”‹•–‹ „‡–™‡‡ –™‘ •—”ˆƒ ‡• ‹ ‘–ƒ – ƒ† ‹• Šƒ”ƒ –‡”‹œ‡† „› –Š‡
•—”ˆƒ ‡ ‘”’Š‘Ž‘‰›Ǥ ”‹ –‹‘ ‹• ƒ ˆ— –‹‘ ‘ˆ ‘–ƒ – ’”‡••—”‡ ƒ† •—”ˆƒ ‡ ”‘—‰Š‡••Ǥ ‹–Š ƒ ˆ‡™
‡š ‡’–‹‘• ‘ˆ Š‹‰ŠŽ› †‡ˆ‘”ƒ„Ž‡ •—”ˆƒ ‡•ǡ ˆ”‹ –‹‘ ‹• ‹†‡’‡†‡– ‘ˆ ‘–ƒ – ƒ”‡ƒǤ ”‹ –‹‘ ‹• ƒ
ˆ— –‹‘ ‘ˆ –‡’‡”ƒ–—”‡ǡ ‡•’‡ ‹ƒŽŽ› ˆ‘” ‡–ƒŽ•ǡ ‹– ‹ ”‡ƒ•‡• ™‹–Š –‡’‡”ƒ–—”‡Ǥ ‘” ƒŽŽ ‡‰‹‡‡”‹‰
’—”’‘•‡•ǡ –Š‡ †›ƒ‹ ˆ”‹ –‹‘ǡ –Šƒ– ‹•ǡ ˆ”‹ –‹‘ ‘ˆ”‘–‡† „‡–™‡‡ –Š‡ •—”ˆƒ ‡• ™Š‡ ‹ ‘–‹‘ǡ ‹•
’”ƒ –‹ ƒŽŽ› ‘•–ƒ–ǡ –Š‘—‰Š ƒ– Š‹‰Š ˜‡Ž‘ ‹–‹‡• ‹– –‡†• –‘ †‡ ”‡ƒ•‡ „› ƒ •ƒŽŽ ˜ƒŽ—‡Ǥ
‡– —• ‘•‹†‡” ƒ ‘„Œ‡ – ‡’– ‘ ƒ ”‘—‰Š •—”ˆƒ ‡ǡ ƒ• ™‡ –”› –‘ ‘˜‡ –Š‡ ‘„Œ‡ –ǡ ˆ”‹ –‹‘ †‡˜‡Ž‘’•
‘’’‘•‹‰ –Š‡ ‘–‹‘Ǥ Š‹• ‘’’‘•‹–‹‘ ‰”‘™• ƒ• –Š‡ ƒ’’Ž‹‡† ˆ‘” ‡ †‘‡•Ǥ – ‘‡ ’‘‹– ˆ”‹ –‹‘ ƒ ‘
Ž‘‰‡” ‘’’‘•‡ ‘–‹‘ǡ ƒ† –Š‹• ’‘‹– ‹• –Š‡ ’‘‹– ‘ˆ ƒš‹— •–ƒ–‹ ˆ”‹ –‹‘Ǥ ˆ–‡” –Š‹• ’‘‹–ǡ
ˆ”‹ –‹‘ ‘‡• †‘™ „› ƒ •ƒŽŽ ˜ƒŽ—‡ ƒ† •—•–ƒ‹• ƒ• –Š‡ ‘–‹‘ ‘–‹—‡•Ǥ Š‡ ƒˆ‘”‡‡–‹‘‡†
ˆƒ – ‹• ‰”ƒ’Š‹ ƒŽŽ› ”‡’”‡•‡–‡† ‹ ȏ ‹‰ ʹǤͷ͵Ȑ

[Fig 2.53: Variation of friction force with applied force]

The friction force can be represented as, a product of normal contact force between the contact
surfaces and coefficient of friction, indicated by Greek symbol ‘μ’.

QP No. SSC/Q4401, Version 1.0, NSQF Level 7, Compliant with Aero and Auto Industries, Page 61 age 61
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