156 Complementary Experimental Physics
Procedure
The experiment is done in two stages.
I. To standardise the potentiometer
Make the connections as shown in figure. An accumalator E, a key Kand a rheostat
Rh is connected in series across the potentiometer wire AB. The Daniel cell of emf
1.08V is connected with the positive end A of the potentiometer wire and negative
pole to galvanometer G and a jockey J.
The key K is closed. The rheostat is adjusted to send a suitable current through
the circuit. The jockey is moved over the potentiometer wire and the balancing length
Lis measured. Thus the potentiometer is standardised. Standardise the potentiometer
to asmall value of p.d per cm. For this adjust the rheostat to get balancing length on
the last wire,then Rh should not be disturbed.
II. Measurement of V
Nowremove the Daniel cell and the galvanometer from the secondary circuit.
Then connect the given low range voltmeter which is to be calibrated between the
point Aand the jockey J. Do not disturb the primary circuit. The jockey is moved
along the potentiometer wire so that the voltmeter reads 0.11V (V). The corresponding
length I of the potentiometer wire from the end Ais noted. The p.d across the length
1.081
is calculated by using V = The difference between V and V, gives the
correction to the voltmeter reading V The jockey is then moved along the wire
such that the voltmeter reads 0.2, 0.3, 0.4 ... volts. In each case the length of the
potentiometer wire is noted and calculate V. The correction V- V, is calculated in
each case. Acalibration graph is drawn with voltmeter reading V, along the X-axis
and the correction (V-V) along the Y-axis.
Result
The given voltmeter is calibrated and calibration graph is drawn.
Complementary Experimental Physics 157
EXPERIMENT NO. 21
MOMENT OF INERTIA OF AAFLYWHEEL
Aim
To determine the moment of inertia of the flywheel.
Apparatus
The mounted flywheel, slotted weights, string and a stop watch.
Aflywheel is aheavy wheel (W) which has along cylindrical axle passing through
its centre. The horizontal axle is mounted between two vertical supports on ball
bearings. The centre of gravity of the system lies on its axis of rotation so that when
mounted on ball bearings, it can be made to rest at any position. There is a small peg
pon the axle. One end of the string is attached to the peg and the string is wound
round over the axle. The other end of the string carries a weight hanger. There is a
the
long horizontal pointer fitted on one of the vertical support and the other end of
pointer is close to the rim of the wheel.
poiFter W
Axle
h
Ground
Theory attached to the peg p. The
Let a mass M be attached to a string and the other end is
is at a height h above the
string is wound round the axle Such hat the mass M
the mass to descend. When the
ground. The fly wheelis given a rtation by allowing
potential energy of mass M = M¡h
mass M reaches the ground, the loSS In
188 Complementary Eayerimental Physics Complementery Esperimemtal Physics
This loss in potentialenergy is uilised for )imparting kinetic energy of rotation
Mvand 3)to do
M(2gh-ro) Mn (Zgh
lo'othe wheel 2) imparting kinetic energy to the mass (Z)
work against friction, IfWbe the work done against friction for onerotation, then All thequantities on the R.HS are
known ecent . If we can find out , the
the total work done against friction is NW, Where Nis the number of rotations made moment of inertia Iof the flywheel can be
by the wheel before the mass is just released. To determine the value of . we note the evaluated.
time t. the wheel takes to come to rest
Using law of conservation of energy we have. after the mass gets detached. Considering the retardation due to friction to be uniforn
loss in potential energy = gain in K.E of the wheel + gain in K.E of the mass + the average angular velocity = Zan
work done against friction.
i.e. 4nn
Mgh la'M' NW ...*.*..)
Observations and tabulations
If the wheel makes n rotations before coming to rest after the mass has been Vernier calipers readings
detached from the axie then the workdone against friction is n W. This must be Magnitude of one main scale division (ms.d) =
equal to the kinetic energy of rotation. Number of vernier scale divisions n
L.e. = nW Valueof one m.s.d
Least count of the vernier (L.C)
e..Cm
or W
2 To find the radius of the axle (r)
Putting this in equation (1), we get
Trial M.S.R V.S.R Total reading = M.S.R +Mean diameter
NIa' (V.S.R L.C) d in cmn
(cm) (divisions)
Mgh = lo' + Mv+ 2n
No.
Mgh =
Ifr is the radius of the axle, then v = Io.
Thus, Mgh
d
Cm
Mean radiusr=
M(2gh -ro') =
160 Complementary Experimental Physics Complementary Experimental Physics 161
Observations with the flywheel Procedure
To begin with the flywheel is set into motion and then stopped. This is
Number
Time
few times. Astring of suitable length is taken. The length is so chosen that repeated a
it is equal
Height of of
taken to to the height of the axle from the ground. A mass M is attached to one end of the
SI.
No.
Mass
suspended
mass
from Numberrotations stopdetachaftero= 4nnMoment Mn (2gh
of made of
string. The other end of the string is attached to the peg on the axle. The string is
wound over the axle uniformly several times by manually rotating the flywheel. The
Mkg. ground rotations before ment t' rad/s inertia N+n
'h' (m) N
stopping mass is kept properly supported at aknown height hfrom the floor.
(s
n
The mass Mis released and allowed tofall. The string unwinds from the axle and
finally gets detached from the peg. The number of rotations N made by the wheel
before the peg detached is noted. This is nothing but the number of winding made
over the axle.
2
When the string just detached from the axle simultaneously start a stop watch.
3 The number of rotations made by the wheel n, and the time taken t for the fly wheel
4zn
is evaluated. the
4
to stop are noted. From n and t, the angular velocity =
5 radius r of the axle is found out by using vernier calipers. Assuming the value of g as
9.8 ms the moment of inertia of flywheel can be evaluated.
The experiment is repeated by varying the mass Mand height h. For the same
be repeated for three different
Mean moment of inertia, I= mass two different heights can be chosen and it can is taken.
.kgm² masses. In each case I is calculated and the mean value
Result
the fly wheel = . kgm²
The moment of inertia of
Working Formula
Mn 2gh -r
I=.
N+n
