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

‘•‹†‡” ƒ ›Ž‹†‡” ”‘ŽŽ‹‰ †‘™ ƒ ‹ Ž‹‡† ’Žƒ‡ǡ ƒ• •Š‘™ ‹ ȏ ‹‰ ʹǤ͸ͳȐǤ Š‡ ˆ‘” –Š‡ •ƒ‡ ‹•
ƒ• •Š‘™Ǥ ‹† –Š‡ ƒš‹— ˆ”‹ –‹‘ ‘‡ˆϐ‹ ‹‡– ”‡“—‹”‡† –‘ ’”‡˜‡– –Š‡ ›Ž‹†‡” ˆ”‘ •Ž‹†‹‰Ǥ

[Fig 2.61: cylinder rolling down an inclined plane]

The torque required to provide angular inertia for the cylinder is: T = Iα

From [Fig 2.62], we could observe the following:

[Fig 2.62: maximum velocity (v) and acceleration (a) of a rolling cylinder]

Ø The point of contact of cylinder with the inclined surface is the instantaneous center of
rotation and has to be characterized by zero velocity and zero acceleration.

Ø Any other point away from the instantaneous center of rotation will have velocity
proportional to ‘ω’ and acceleration proportional to ‘α’.

Ø The highest point will have twice the velocity and acceleration than that of the center of
mass.

Page 70 QP No. SSC/Q4401, Version 1.0, NSQF Level 7, Compliant with Aero and Auto Industries,