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

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

[Fig 2.59: rolling of rigid body]

The velocity at ‘B’ perpendicular to ‘OB’ is given by: [ω ∗ OB] = ω ∗ 2r cos θ

This could also be proved by the law of parallelogram of vectors, given by:

2
2
2
2
Resultant = V cm + ωr + 2 ωr ∗ V cm ∗ cos 2θ = ωr + ωr + 2 ωr ∗ ωr ∗ cos 2θ
Resultant = ωr ∗ 2 + 2 cos 2θ = ωr ∗ 2(1 + cos θ − sin θ = ωr ∗ 4 cos θ
2
2
2
Therefore, we have: Resultant = ωr ∗ 2 cosθ

Page 68 QP No. SSC/Q4401, Version 1.0, NSQF Level 7, Compliant with Aero and Auto Industries,