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Gyroscope

This document provides instructions for performing an experiment using a motorized gyroscope. The aim is to verify the rules of gyroscopic precession. Key points: 1) A spinning disc or gyroscope experiences precession when a torque is applied perpendicular to its axis of spin. This causes it to rotate about a third axis perpendicular to both the axis of spin and torque. 2) The experiment involves applying varying loads and speeds to the gyroscope and measuring the resulting angle of precession over time. 3) Formulas are provided to calculate the angular velocity of precession from the rate of change of the angle of precession over time measured in the experiment.

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144 views6 pages

Gyroscope

This document provides instructions for performing an experiment using a motorized gyroscope. The aim is to verify the rules of gyroscopic precession. Key points: 1) A spinning disc or gyroscope experiences precession when a torque is applied perpendicular to its axis of spin. This causes it to rotate about a third axis perpendicular to both the axis of spin and torque. 2) The experiment involves applying varying loads and speeds to the gyroscope and measuring the resulting angle of precession over time. 3) Formulas are provided to calculate the angular velocity of precession from the rate of change of the angle of precession over time measured in the experiment.

Uploaded by

muralidharan
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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MANUAL

FOR

MOTORIZED GYROSCOPE
MOTORISED GYROSCOPE

Aim: To verify the gyroscopic rules of a plane rotating disc

Definitions:

Axis of Spin: If a body revolving about an axis, the latter is known as axis of spin

Gyroscopic effect:

To a body revolving about an axis say OX, if a couple which can be represented by a vector OY
perpendicular to Ox is applied, then the body tries to process about an axis Oz, which is
perpendicular both to OX and OY. Thus the plane of spin, plane of precession and the plane of
gyroscopic couple are mutually perpendicular. The above combined effect is known as
Processional or Gyroscopic effect

Precession:

Precession means rotation about the third axis OZ, which is perpendicular to both the axis of
spin OX and that of the couple OY.

Axis of precession:

The third axis OZ about which a body revolves and is perpendicular to both the axis of spin
Ox and that of the couple OY is known as Axis of Precession
Gyroscope:

Gyroscope is a body while spinning about an axis is free to move in other directions under the
action of external forces

E.g.: Locomotive Automotive and Aero plane making a turn. In certain cases the gyroscopic
forces are undesirable where as in other cases the gyroscopic effect can be used for developing
desirable forces.

Gyroscopic couple of a plane of disc:

Let a disc of weight w and having a moment of inertia I be spinning with an angular velocity ω
about axis ox in an anticlockwise direction viewing from the front. Therefore the angular
momentum of disc is I.ω. applying right hand screw rule, the sense of vector representing the
angular momentum of disc which is also a vector quantity will be in the direction ox as shown.
A couple, whose axis is OY and is in the plane xoz, is now applied to process the axis ox.

Let axis ox turn through a small angular displacement from OX to OX’ in time δt. The couple
applied produces a change in the direction of angular velocity, the magnitude remaining
constant. This change is due to the velocity of precession.
Technical data:

Weight of the rotor: 7Kg

Rotor diameter: 300mm

Rotor thickness: 8mm.

M.I of the disc:

Distance of bolt center of weight pan from disc center:

Procedure:

 Switch on the supply.

 Set the required speed by the regulator as constant.

 Add the load viz 1/2kg, 1kg…

 Loose the lock screw, start the stopwatch and note down.

 Watch the angular displacement at particular time interval. Take the readings for
different loads. Repeat the experiment maintaining load as constant and varying the
speed.
Tabulation:

Constant speed method:

ω=2πN/60.

SI.No Weight Angle of Time taken dθ/dt Percentage


applied precession for error
precession
C=Iωωp

Constant Load method :

Sl.No rpm Angle of Time taken dθ/dt Percentage


precession for error
precession
C=Iωωp
Formula:

ω=2πN/60.

ω-Angular velocity.

N- speed of the rotor.

C=I ωωp.]

Angular velocity of precession , ωp=dθ/dt

W = weight of the disc

r = distance of weight pan bolt center to disc center

I= Moment of inertia of the rotating disc (I=mr2/2 Kgm2)

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