Gyroscope

• Gyroscope is a mechanical arrangement consisting of a rotor which spins at high speed about its axis and being free to turn in any direction.

• It consists of following parts:**

1. Rotor.

2. Axle.

3. Inner gimble.

4. Outer gimble.

5. Bearings.

6. Frame.

• It consists of a rotor rotating on an axle which is supported by a ring called inner gimble, with bearings. This inner gimble is supported in one more ring called outer gimble, with bearings; and this outer gimble is supported inside a frame, with bearings. The frame is supported on a heavy stand.

Terminology used in ship:

1] Bow End: It is the front end of the ship.

2] Stern End : It is the rear end of the ship.

3] Star board: It is the right hand side of the ship when seen from rear end.

4] Port end: It is the left hand side of the ship when seen from rear end.

5] Steering: It is turning of complete ship in a curve towards the left or right.

6] Pitching of ship: It is the cyclic up and down motion of bow and stern.

7] Rolling of ship : It is the cyclic up and down motion of port and starboard side.

1. Initial Angular momentum of Disc: At initial position (i.e. spin axis is OX), the magnitude of angular momentum of disc is $IW$. We know that, angular momentum is a vector quantity, using right hand rule it is represented by $\overrightarrow{OX}$.

2. Final Angular momentum of Disc: After small interval of time ‘$\delta t’$ the final position of the spin axis is $OX’$. At this instant, angular momentum of disc remains same i.e. $IW$. Using right hand rule, it is represented by $\overrightarrow{OX}$.

3. Change in Angular momentum of Disc: Change in angular momentum = $\overrightarrow {ox'} - \overrightarrow {ox}$

= $\overrightarrow {xx'}$

= $\overrightarrow {ox'} . \delta \theta$

= $Iw. \delta \theta$

4. Gyroscopic couple on Disc:

Rate of change of angular momentum = $IW. \frac{\delta \theta}{\delta t}$

This rate of change of angular momentum will result due to application of couple to a disc. Therefore, the couple applied to the disc for causing procession is given by,

$C = \lim_{\delta t \to\ 0} \ IW. \ \frac{\delta \theta}{\delta t} \ = \ IW. \ \frac{d \theta}{dt}$

$C = Iw. W_p$ -------[A]

Couple given by equation [A] is known as Gyroscopic couple.