- A gyroscope is a device that maintains orientation based on angular momentum. It has a spinning wheel or disk mounted on gimbals to minimize external torque and keep its orientation nearly fixed regardless of motion. - Precession is the change in the axis of spin of a rotating body in response to an external torque. This results in two components of angular acceleration - one parallel and one perpendicular to the original axis of spin. - A gyroscopic couple is produced on a spinning object when its axis of spin rotates about another axis. This couple depends on angular velocity and moment of inertia and can cause a rotating object like a ship or airplane to tilt when turning or pitching.

1. Gyroscope
• A gyroscope is a device for measuring or maintaining
orientation, based on the principles of angularmomentum.
• Mechanically, a gyroscope is a spinning wheel or disk in which
the axle is free to assume any orientation. Although this
orientation does not remain fixed, it changes in response to an
external torque much less and in a different direction than it
would without the large angular momentum associated with the
disk's high rate of spin and moment of inertia.
• Since external torque is
minimized by mounting the
device in
orientation
gimbals,
remains
its
nearly
fixed, regardless of any
motion of the platform on
which itis
mounted.
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2. PrecessionalAngularMotion
(V
ectorialrepresentation of angularmotion)
• W
eknow that the angularaccelerationisthe rate of change
of angularvelocity with respect totime.
• It isavector quantity and may be represented by
drawingavector diagramwith the help of right handscrewrule.
• Consider a disc, as shown in Fig. (a), revolving or spinning about the axis
OX (known as axis of spin) in anticlockwise when seen from the front,
with an angularvelocity in aplaneat right anglesto thepaper.

3. • After ashortintervalof time t,letthediscbespinningaboutthenewaxisofspin
OX’(atan angle ) with anangular velocity ( + ).
• Usingthe right handscrewrule, initial angularvelocity of the disc isrepresented by
vector ox;and thefinalangularvelocityofthedisc( + )is representedby vector ox’as
showninFig.(b).
• Thevectorxx’representsthechange ofangularvelocity in time t i.e.theangular acceleration
ofthedisc.Thismay beresolvedintotwocomponents,oneparallelto oxandtheother
perpendiculartoox.
5

4. • where d /dtistheangularvelocityoftheaxisofspinabouta certain
axis, whichis perpendiculartothe plane in which the axis of spin is
goingto
rotate. 36
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6. GyroscopicCouple
• Consideradiscspinning with anangular velocity rad/s about the axisofspin OX,
inanticlockwisedirectionwhenseenfromthefront,asshowninFig.
• SincetheplaneinwhichthediscisrotatingisparalleltotheplaneYOZthereforeit iscalled
planeofspinning.
The plane XOZ is a horizontal plane and the
axis of spin rotates in a plane parallel to the
horizontalplaneabout an axisOY
.
Inotherwords,theaxis ofspin is said tobe
rotatingor processing about an axisOY
.
In otherwords,theaxisofspin is said tobe
rotatingabout an axisOY(whichis
perpendiculartoboththeaxes OX and OZ)at
an angular velocity prad/s.
ThishorizontalplaneXOZis calledplaneof
precessionand OYis theaxisofprecession.

7. • Sincethe angular momentum isavector quantity, therefore itmaybe represented
bythe vector OX,as shown inFig.
• TheaxisofspinOXisalsorotatinganticlockwisewhenseenfromthetopaboutthe axisOY
.
• Lettheaxis OX isturnedintheplaneXOZthrougha smallangle radianstothe position OX',
intime t seconds.Assumingtheangularvelocity tobeconstant,the angularmomentum will
nowberepresentedbyvectorOX’.

8. where p=Angular velocity of precession of the axis
of spin or the speed of rotation of the axis of spin
about the axisof precessionOY
.
InS.I.units, the units of CisN-mwhenIisin kg-m2.
Relationship between force
(F), torque ( ), momentum
(p), and angularmomentum
(L)vectors in arotating
system,r= Positionvector

9. Effectof the Gyroscopic Couple on an
Aero-plane
• Thetop andfront view of anaero-plane areshown in Fig.
• Letengineorpropellerrotates in the clockwise direction whenseenfrom the rear or tail
endandthe aero-planetakesaturn to the left.

10. Effectof the Gyroscopic Couple on an
Aero-plane

11. Effectof the Gyroscopic Couple on an
Aero-plane

12. • Thetop and front viewsof anavalship are shown in Fig. The
fore end of the ship iscalled bow and therear end is known as
sternor aft.Thelefthandand righthandsidesoftheship,when
viewed from the stern are called portand star-boardrespectively.
• Theeffect of gyroscopiccoupleon the navalship will occur in
the following threecases:
1. Steering
2. Pitching,and
3. Rolling
Effectof theGyroscopic Coupleon a
Navel Ship
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13. Effectof Gyroscopic Couple on a
Naval Ship during Steering
• Steering is the turning of a complete ship in a curve towards left
or right, while itmovesforward.

14. Effectof Gyroscopic Couple on a Naval Ship
duringSteering
S. No. View Point Direction of
rotor direction
Turn Effect
1 Stern Clockwise Left Bow raised Stern depressed
2 Stern Clockwise Right Bow depressed Stern raised
3 Stern Anticlockwise Left Bow depressed Stern raised
4 Stern Anticlockwise Right Bow raised Stern depressed
5 Bow Anticlockwise Left Bow raised Stern depressed
6 Bow Anticlockwise Right Bow depressed Stern raised
7 Bow Clockwise Left Bow depressed Stern raised
8 Bow Clockwise Right Bow raised Stern depressed

15. Effectof Gyroscopic Coupleon a
Naval Ship duringPitching
• Pitching is the movement of acomplete ship up
and down in avertical plane about transverse axis,
asshown in Fig.

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17. Effectof Gyroscopic Coupleon a Naval Ship
duringPitching
S. No. Pitching View Point Direction of
rotor direction
Effect
1 Upward Stern Clockwise Ship turn towards star board side
2 Upward Stern Anticlockwise Ship turn towards port side
3 Upward Bow Clockwise Ship turn towards port side
4 Upward Bow Anticlockwise Ship turn towards star board side
5 Downward Stern Clockwise Ship turn towards port side
6 Downward Stern Anticlockwise Ship turn towards star board side
7 Downward Bow Clockwise Ship turn towards star board side
8 Downward Bow Anticlockwise Ship turn towards port side

18. Effectof Gyroscopic Coupleon a Naval
Ship duringRolling
• W
e know that, for the effect of gyroscopic couple to occur, the
axis of precessionshould alwaysbe perpendicular to the axisofspin.
• If, however, the axis of precession becomes parallel to the axis
of spin, there will be no effect of the gyroscopic couple acting
on the body of theship
• In caseof rolling of aship, the axis of precession (i.e.
longitudinal axis)isalwaysparalleltothe axisof spin for all
positions.
• Hence, there is no effect of the gyroscopic couple acting on
the body of aship during rolling.