Define Gyroscopic Couple with example

Gyroscopic Couple:

Consider a disc spinning with an angular velocity ω rad/s about the axis of spin OX, in anticlockwise direction when seen from the front as shown in fig:

Since the plane in which the disc is rotating is parallel to the plane YOZ, therefore it is called plane of spinning. The plane XOZ is a horizontal plane and the axis of spin rotates in a plane parallel to the horizontal plane about an axis OY.

In other words, the axis of spin is said to be rotating or processing about an axis OY which is perpendicular to both axes OX and OZ at an angular velocity ωp rad/s. This horizontal plane XOZ is called plane of precession and OY is called the axis of precession.

Let I = Mass moment of inertia of the disc about OX and

ω = Angular velocity of the disc.

∴ Angular momentum of the disc = I.ω

In SI units, the units of Gyroscopic Couple is N.m when I is kg-m2. It may be noted that –

1. The couple I.ω.ωp, in the direction of the vector xx’ (representing the change in angular momentum) is the active gyroscopic couple. It has to be applied over the disc when the axis of spin is made to rotate with angular velocity ωp about the axis of precession.

2. When the axis of spin itself moves with angular velocity ωp, the disc is subjected to reactive couple whose magnitude is same. But opposite in direction to that of active couple. This reactive couple to which the disc is subjected when the axis of spin rotates about the axis of precession is known as reactive gyroscopic couple. The axis of the reactive gyroscopic couple is represented by OZ’.

3. The gyroscopic couple is usually applied through the bearings which support the shaft. This bearings will resist equal and opposite couple.

4. The gyroscopic principle is used in an instrument or toy known as gyroscopic. The gyroscopes are installed in ships in order to minimize the rolling and pitching effects of waves. They are also used in aeroplanes, monorail cars, gyro-compasses, etc.