Moment of Inertia of a flywheel

1. Hanish -243/C/10
Gurmeet Singh-242/C/10
Gaurav Rana- 241/C/10
Digvijay-240/C/10

2. To determine the moment of inertia of a
flywheel about its own axis of rotation.

3. The flywheel, weight box, thread, stop-
watch, metre scale and vernier calipers.

4.  Flywheel is simply a heavy wheel with a long
axle which when properly supported in
bearings may remain at rest in any position,
i.e., its centre of gravity lies on the axis of
rotation.
 Its moment of inertia can be determined
experimentally by setting it in motion with a
known amount of energy.

6.  The flywheel is mounted in its bearings with
its axle horizontal and at a suitable height
from the ground.
 A string carrying a suitable mass m at its one
end and having a length less than the height
of the axle from the ground, is wrapped
completely and evenly round the axle.
 When the mass m is released, the string
unwinds itself, thus setting the flywheel in
rotation.

7.  As the mass descends a distance h, it loses
potential energy mgh which is used up partly in
a. providing kinetic energy of translation
(½mv2)
b. giving kinetic energy of rotation to the
flywheel (½Iω2)
c. doing work against friction (n1F).
Hence , mgh = ½mv2 + ½Iω2 + n1F.

8.  After the mass has detached, If flywheel
makes n2 rotations in this time, the work
done against friction is equal to n2F and is
equal to the kinetic energy of the flywheel at
the instant the mass drops off.
 Thus n2F = ½Iω2 .
 Hence I = m(2gh/ω2-r2 )
1+n1/n2

9.  If the force of friction is steady, the motion of
the flywheel is uniformly retarded and the
average angular velocity during this interval is
equal to ω/2.
 Thus
ω/2 = 2πn2/t

10.  Take a string of length less than the height of the
axle from the floor. Wrap the string evenly round
the axle until the projecting peg is horizontal and
make a mark on the string where its contact with
the axle just ceases.
 Let the mass be released. Count the no. of
rotations n1, the flywheel makes before the loop
comes off the peg and the mass drops off.
Carefully start the stopwatch at the moment the
mass detaches and also continue to count the no.
of rotations n2 the flywheel makes before it
comes to rest.

11.  Stop the stopwatch when the flywheel finally
comes to rest and thus determine the value of
t, the interval for which the flywheel
continues to rotate after the detachment of
the mass.
 Measure the length of the string between the
loop and the mark at the other end which
gives h. With the help of a vernier calipers,
calculate the mean radius of the axle.

12.  Repeat the experiment with different masses
and strings of different lengths and take at
least three sets of observations, and in each
set for the same value of m and h take at
least three observations, calculate the mean
values of n1,n2 and t.
 Calculate the moment of inertia of flywheel
for each set of observations separately and
find out the mean value of moment of inertia
of the flywheel about its axis of rotation.

13.  The length of the string should be always less than
the height of the axle of the flywheel.
 The loop slipped over the peg should be quite
loose so that when the string has unwound itself.
 The string should be evenly wound on the axle,
i.e., there should be no overlapping of, or a gap
left between, the various coils of the string.
 The winding should be stopped, when almost
complete the projecting peg is horizontal.
 To determine h, measure only the length of the
string between the loop and the mark at the other
end, where the string left the axle before the start
of the flywheel.

14. Set No.
Reading along
any diameter
a(cm)
Reading along
perpendicular
diameter
b(cm)
(a+b) /2
1 2.1 2.1 2.1
2 2.1 2.2 2.15
3 2.0 2.1 2.05
Mean Diameter 2.1

15. Set no. m(gm) h(cm) n1 n2 t(sec) ω
(sec-1)
I
(kg m2)
1 500 19.8 3 30 42.66 8.83 0.02
2 500 26.4 4 39 46.13 10.62 0.02
3 1000 19.8 3 57 55.70 12.86 0.02
4 1000 26.4 4 75 63.62 14.81 0.02

16.  Mean corrected radius of axle = 1.05 cm
 Mean Inertia ,I=(0.02+0.02+0.02+0.02)/4
=0.02 kg m2

17. The moment of inertia of the flywheel about its
axils of rotation = 0.02 kg m2

18.  The exact instant at which the mass drops off
can’t be correctly found out and hence the values
of n1,n2 and t can’t be determined very
accurately.
 The angular velocity ω of the flywheel has been
calculated from the formula ω = 4πn2/t on the
assumption that the force of friction remains
constant while the angular velocity of the
flywheel decreases from ω to zero. But as the
friction is less at greater velocities, we have no
justification for this assumption.
 Hence for more accurate result, ω should be
measured by a method in which no such
assumption is made e.g. with a tuning fork.