Page 67 - C:\Users\trainee\AppData\Local\Temp\msoEAA3.tmp

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

ʹǤ͹Ǥͳ —”‡ ‘ŽŽ‹‰

‘ŽŽ‹‰ ‹• ƒ ’Š‡‘‡‘ Šƒ”ƒ –‡”‹œ‡† „› –™‘ †‡‰”‡‡• ‘ˆ ˆ”‡‡†‘ǡ ƒ‡Ž›ǡ –”ƒ•Žƒ–‹‘
ƒ† ”‘–ƒ–‹‘Ǥ Š‹• ‹• —•‡ˆ—Ž ‘– Œ—•– ˆ‘” ƒƒŽ›œ‹‰ ™Š‡‡Ž †›ƒ‹ • ‘ˆ ƒ ˜‡Š‹ Ž‡ǡ „—– ƒŽ•‘ ˆ‘”
ƒƒŽ›œ‹‰ ‡ Šƒ‹•• •— Š ƒ• ˆ”‹ –‹‘ ™Š‡‡Ž•ǡ ‰‡ƒ”•ǡ ‡– Ǥ

‡– —• •–ƒ”– „› ‹–”‘†— ‹‰ –Š‡ ‘ ‡’– ‘ˆ ‹•–ƒ–ƒ‡‘—• ‡–‡” ‘ˆ ”‘–ƒ–‹‘Ǥ
Š‡ ˜‡Ž‘ ‹–› ƒ– –Š‡ ‹•–ƒ–ƒ‡‘—• ‡–‡” ‘ˆ ”‘–ƒ–‹‘ǡ ƒ• •Š‘™ ‹ ȏ ‹‰ ʹǤͷͺȐ ‘’”‹•‡• ‘ˆ
–™‘ ‘’‘‡–•ǣ

[Fig 2.58: pure rolling]

1) Since the cylinder is rigid, all the points on the cylinder have the same velocity as that of
V CM .

2) The angular velocity ω contributes to the second component, which is ω × r , where ‘r ’
is the position vector and is always directed from the center of rotation to the point of
interest.

Hence, the velocity of the instantaneous center of rotation is given by:

V = V CM + ω × r = [V CM i + (ω(−k) × r −j = [V CM i + ω −k × r −j = V CM − ωr i
Ic
Since the velocity at the instantaneous center is zero, as have: V CM − ωr i = 0 = V CM = ωr
In an ideal rolling situation, where ω and (V) are kept constant, the static friction at the point of
contact is zero.

QP No. SSC/Q4401, Version 1.0, NSQF Level 7, Compliant with Aero and Auto Industries, P
Page 67 age 67
Copyright Diary No – 9119/2018-CO/L