1) The document describes an experiment to determine the moment of inertia of a flywheel about its axis of rotation. A known mass is attached to a string looped around the flywheel's axle. 2) As the mass falls, it causes the flywheel to rotate. The number of revolutions is recorded. Using equations that relate the kinetic energy of the mass and flywheel to the potential energy lost by the mass, the moment of inertia can be calculated. 3) The procedure involves allowing the mass to fall and detach from the axle, recording the revolutions and time taken for the flywheel to stop rotating, and using the data in equations to determine the moment of inertia.

1. CENTURION UNIVERSITY OF TECHNOLOGY AND MANAGEMNT
MECHANICS FOR ENGINEER
TOPIC: the moment of inertia of a
flywheel
NAME: - KALINGO AUROBINDO NAYAK
SEC- D REG NO-200101120022
BRANCH: -CSE
CAMPUS: -PARALAKHEMUNDI

2. AIM: To determine the moment of inertia of a fly wheel
about its axis of rotation
APPARATUS REQUIRED: Flywheel, stop-watch, a known
mass meter scale and Vernier calipers.
DESCRIPTION: The flywheel consists of a massive wheel
W with a long horizontal axle on either side supported on
ball bearings embedded in a bracket. The base of the
bracket is fixed to a rigid support like a wall.
A short peg A project from the axel. The free end of a string carrying a mass m
is looped over the peg and the length of the string is so adjusted that the loop slips off the peg
automatically when the mass touches the ground. The flywheel is turned so that the string is wrapped
round the axel evenly without any overlapping.
THEORY: Let be the height through which the mass descends, 1
the number of revolutions made by the wheel before the mass
just touches the ground. The potential energy lost by the mass
in descending the distance is, where g is the acceleration due to
gravity. This energy is utilized in three way.
(i) The energy 2 to the falling mass, where is the final velocity of
the mass just before it touches the ground,

3. (ii) imparting kinetic energy 2 to the wheel is the moment of
inertia of the flywheel about the axis of rotation and the
angular velocity of the flywheel at the moment just when the
mass touches the ground and
(iii) Overcoming the friction 1 in the bearings, where is the
amount of work done against friction for each revolution of the
wheel
Hence by the principal of conservation of
Energy.
But where r is the radius of the axel. …….. …….
………… (1)
Value of - Let the wheel make 2 revolutions
before it comes to rest after the loop slips off
the peg. Then the average angular velocity=.
Since the wheel is retarded uniformly on
account of friction, the average angular velocity
is ()/2. ……… ………. …………. (ii)
Value of f: The kinetics energy of the wheel is
utilized in overcoming friction during these
revolutions. ……… ………. ……… (iii)

4. From (i) and (ii)
PROCEDURE: 1) Fix one of end of the string into
the axle and turn it around such that when the
suspended mass at the other end of the string
reaches the floor, the string becomes detached
from the axle (so it allows the wheel to revolve
freely).
2) Record the number of revolutions, n1 during
the falling of the mass.
3) Record the time, t, and number of
revolutions (including fractional revolution)
after the string had been detached until the
wheel comes to rest.
4) To estimate the extent of incomplete
revolution, use a thread to measure the
distance along the circumference of the wheel
by which the mark has advanced beyond the
pointer. Divide the distance by the

5. circumference of the wheel. Add this result to
get the number of complete revolutions.
5) Calculate the angular velocity, ω, from
equation (ii).
6) Knowing m, h, n2, r, and ω substituting
these values in equation (4), the moment
inertia, I, can be determined.
7) Repeat the process twice for same height
and load
8) Repeat the process for different n1 and h.
Observations:
Mass attached tothestring (m)=400gms.
Mean diameter ofaxel(d)= 2.6cms
Mean radius oftheaxel(r)=d/2 =1.3cms
Circumferenceoffly wheel (s)=14cms
TABULATION: -

6. Result
Moment of inertia of the fly wheel =.4218.45.67......gm.cm2
Precautions:
1.The string should woundround theaxel evenly without any overlapping.
2.The loop slipped on thepegshould beloose.
3.The flywheel should start ofits ownaccord under theaction ofthemass
attached toit

7. without giving any push.