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**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:**

Rotor.

Axle.

Inner gimble.

Outer gimble.

Bearings.

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.