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

2.9 Gyroscopic Couple

Let us consider a pseudo effect, which is generally called the gyroscopic effect. This effect is brought
about, whenever the direction of the angular momentum changes.

The gyroscopic effect is present in several situations, be it:

Ø Over hung rotor system
Ø Solid axels of a car
Ø Turbo charger system, and more.

Let us understand mathematically and physically the consequences of the gyroscopic effect.

Case 1: Consider a rigid shaft-disc system with a massless shaft and an overhung disc mounted onto
a rotating platform, as shown in [Fig 2.78]. The shaft is given and angular velocity ω , about the
positive ‘x-axis’. The system undergoes an angular precision Ω about the positive ‘y-axis’. Let the
polar mass moment of inertia be (I ) and the diametral mass moment of inertia be (I ).
p
d

[Fig 2.78: shaft disc system spinning and precising about 2 perpendicular axes]

The total angular momentum [Fig 2.79] of the system is given by: I ω i + I Ω j
p
d

[Fig 2.79: direction of spin and precision of the system]

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