DOM MANUAL / B-TECH / MECHANICAL / KUK - TO FIND EXPERIMENTALLY THE GYROSCOPIC COUPLE ON MOTORIZED GYROSCOPE

AIM: TO FIND EXPERIMENTALLY THE GYROSCOPIC COUPLE ON MOTORIZED GYROSCOPE AND COMPARE WITH APPLIED COUPLE.

APPARATUS USED: MOTORIZED GYROSCOPE, TACHOMETER.

INTRODUCTION:

1.      AXIS OF SPAN

IF A BODY IS REVOLVING ABOUT AN AXIS, LATTER IS KNOWN AS AXIS OF SPIN.   

2.      PRECESSION

PRECESSION MEANS THE ROTATION ABOUT THE THIRD AXIS OZ WHICH IS PERPENDICULAR TO BOTH THE AXIS OF SPIN OX AND THAT OF COUPLE OY.

3.      AXIS OF PRECESSION

THE THIRD AXIS OX IS PERPENDICULAR TO BOTH THE AXIS OF SPIN OX AND THAT OF COUPLE OY IS KNOWN AS AXIS OF PRECESSION.

4.      GYROSCOPE

IT IS A BODY WHILE SPINNING ABOUT AN AXIS IS FREE TO ROTATE IN OTHER DIRECTION UNDER THE ACTION OF EXTERNAL FORCE.

EXAMPLE: LOCOMOTIVE, AUTOMOBILE AND AEROPLANE MAKING A TURN. IN CERTAIN CASES THE GYROSCOPIC FORCES ARE UNDESIRABLE WHEREAS IN OTHER CASES THE GYROSCOPIC EFFECT MAY BE UTILIZED IN DEVELOPING DESIRABLE.

5.      GYROSCOPIC EFFECT

TO A BODY REVOLVING ABOUT AN AXIS SAY OX (REFER FIG. 1) IF A COUPLE REPRESENTED BY A VECTOR OY PERPENDICULAR TO OX IS APPLIED, THEN THE BODY TIES TO PROCESS ABOUT AN AXIS OZ WHICH IS PERPENDICULAR BOTH TO OX AND OY. THUS THE PLANE OF SPIN, PLANE OF PRECESSION AND PLANE OF GYROSCOPIC COUPLE ARE MUTUALLY PERPENDICULAR.

THE ABOVE COMBINED EFFECT IS KNOWN AS PROCESSIONAL OR GYROSCOPIC EFFECT.

GYROSCOPIC COUPLE OF A PLANE DISC

LET A DISC OF WEIGHT ‘W’ HAVING MOMENT OF INERTIA I BE SPINNING AT AN ANGULAR VELOCITY ABOUT AXIS OX IN ANTI-CLOCKWISE DIRECTION VIEWING FROM FRONT (REFER FIG.2). THEREFORE THE ANGULAR MOMENTUM OF THE DISC IS I. APPLYING RIGHT HAND , SCREW RULE, THE SENSE OR VECTOR REPRESENTING THE ANGULAR MOMENTUM OR THE DISC WHICH IS ALSO A VECTOR QUANTITY WILL BE IN THE DIRECTION OX AS SHONE . A COUPLE WHOSE AXIS IS OY PERPENDICULAR TO OX AND IS THE PLANE Z, IS NOW APPLIED TO PROCESS THE AXIS OX.

LET AXIS OX TURN THROUGH A SMALL ANGULAR DISPLACEMENT FROM OX TO OX’ IN TIME Δ T. THE COUPLE APPLIED PRODUCES A CHANGE IS DUE TO THE VELOCITY OF PRECESSION. THEREFORE OX REPRESENTS THE ANGULAR MOMENTUM AFTER TIME Δ T.

CHANGE OF ANGULAR MOMENT = OX’-OX =XX’

OR RATE OF CHANGE OF ANGULAR MOMENTUM= ANGULAR DISPLACEMENT/TIME

= XX’/T = OX* ΔΘ/ΔT

AS XX’=OX *Δ Θ IN DIRECTION OF XX’

NOW AS RATE OF CHANGE OF ANGULAR MOMENTUM

=COUPLE APPLIED =C=T

WE GET

T = O × δθ /ΔT

BUT OX = I.Ω

WHERE I = MOMENT OF INERTIA OF DISC AND

Ω = ANGULAR VELOCITY OF DISC. AND IN THE LIMIT WHEN �� IS VERY SMALL, WE HAVE —

Θ/T = DΘ/DT

AND DΘ/DT = ΩP = ANGULAR VELOCITY OF PRECESSION OF YOKE AT VERTICAL AXIS.

THUS WE GET T = I × Ω × WP

THE DIRECTION OF THE COUPLE APPLIED ON THE BODY IS CLOCKWISE WHEN LOOKING IN THE DIRECTION XX AND IN THE LIMIT IS PERPENDICULAR TO THE AXIS OF Ω AND ΩP. THE REACTION COUPLE EXERTED BY THE BODY ON ITS FRAME IS EQUAL IN MAGNITUDE TO THAT OF C, BUT OPPOSITE IN DIRECTION.

RULE NO. 1

“THE SPINNING BODY EXERTS A TORQUE OR COUPLE IN SUCH A DIRECTION WHICH TENDS TO MAKE THE AXIS OF SPIN COINCIDES WITH THAT OF THE PRECESSION”.

TO STUDY THE RULE OF GYROSCOPE BEHAVIOR FOLLOWING PROCEDURE MAY BE ADOPTED:

a)     BALANCE THE INITIAL HORIZONTAL POSITION OF THE ROTOR.

b)     START THE MOTOR BY INCREASING THE VOLTAGE WITH THE AUTO-TRANSFORMER, AND WEIGHT UNTILL IT ATTAINS CONSTANT SPEED.

c)      PRESS THE YOKE FRAME NO.2 ABOUT VERTICAL AXIS BY A APPLIED NECESSARY FORCE BY HAND TO THE SAME (IN THE CLOCKWISE SENSE SEEN FROM ABOVE).

d)     IT WILL BE OBSERVED THAT THE ROTOR FRAME SWINGS ABOUT THE HORIZONTAL AXIS Y.Y MOTOR SIDE IS SEEN COMING UPWARDS AND THE WEIGHT PAN SIDE GOING DOWNWARDS. ROTATE THE VERTICAL YOKE AXIS IN THE ANTI-CLOCKWISE DIRECTION SEEN FROM ABOVE AND OBSERVE THAT THE ROTOR FRAME SWING IN OPPOSITE SENSE (AS COMPARED TO THAT IN PREVIOUS CASE FOLLOWING THE ABOVE RULE).

RULE NO. 2:

“ THE SPINNING BODY PROCESSES IN SUCH A WAY AS TO MAKE THE AXIS OF SPIN COINCIDE WITH THAT OF SPIN COINCIDE WITH THAT OF THE COUPLE APPLIED, THROUGH 90 TURN”

a)     BALANCE THE ROTOR POSITION ON THE HORIZONTAL FRAME.

b)     START THE MOTOR BY INCREASING THE VOLTAGE WITH THE AUTO-TRANSFORMER AND WAIT TILL THE DISC ATTAINS CONSTANT SPEED.

c)      PUT WEIGHT (0.5 KG, 1KG OR 2KG) IN WEIGHT PAN, AND START STOP WATCHTO NOTE THE TIME IN SECOND REQUIRED FOR PROCESSION, THROUGH 60 OR 45 ETC.

d)     THE VERTICAL YOKE PROCESSES ABOUT OZ AXIS AS PER THE RULE NO. 2.

e)     SPEED MAY BE MEASURED BY THE TACHOMETER PROVIDED ON THE CONTROL PANEL.

f)       ENTER THE OBSERVATION IN THE TABLE.

MOTORIZED GYROSCOPE APPARATUS

M WEIGHT OF DISC 4.800 KG

D DIA OF THE PLATE 28.5 CM

DISTANCE WEIGHT POINT TO DISC CENTER 22.5 CM

TIME 60 SEC.

G 9.81 M/S

S. NO.	RPM	Φ2	Φ1	Φ = (Φ2-Φ1)	WT.	I=MXD2/8G	W=(2ΠN/60)	WP=ΠΦ/180T	TTH=IXWXWP	TACT=X DISTANCE
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