MOMENT INERTIA OF A FLYWHEEL LAB REPORT

MOMENT OF INTERTIA

1. MOMENT OF INTERTIA OF AFLYWHEEL.

EGERTON UNIVERSITY
FACULTY OF ENGINEERING AND TECHNOLOGY
DEPARTMENT OF INDUSTRIAL AND ENERGY ENGINEERIG

COURSE: B.Sc. MANUFACTURING ENGINEERING.
COURSE TITLE: MACHINE ELEMENTS 11.
COURSE CODE: MENT 223.
TASK: MOMENT OF INERTIA OF A FLYWHEEL.
NAME: KIPROTICH GARISON.
REG NO. B13/14411/16.
DATE OF SUBMISSION: …26/07 /2018.
SIGN: ………………………
INSTRUCTOR: ENGR.VINCENT ODHIAMBO .

2. MOMENT OF INTERTIA OF AFLYWHEEL.

MOMENT OF INERTIA OF FLYWHEEL
Objective
The objective of this experiment is to determine the relationship between the angular
acceleration of flywheel and the torque producing the acceleration.
Theory
Considering a falling mass,
Net force=mg-F
Acceleration=a
Hence ma=mg-ma
F=m(g-a)
Provided that a is much greater than g.
F=mg
For the wheel,
Angular displacement ϴ=2????????????[????????????�.]
Where N=Number of revolutions.
Average velocity=
1
2
(ϴ+ωN)[rads/s]
Time for N revolution=t seconds.
Therefore,
Angular displacement ϴ=
1
2
ωNt
and ωN=at
hence ϴ=
1
2
at
2


from which a=
4????????????
??????
2

According to the second law of motion, torque producing acceleration =

3. MOMENT OF INTERTIA OF AFLYWHEEL.

Fr=C=K.
4????????????
??????
2

From which K=
????????????
2
4????????????

The constant of proportionality K is called the moment of inertia and may be calculated from the
dimensions and mass of the fly wheel.
K=I=ρπ??????
2
�
°
??????
2
2

Where R= Radius of fly wheel
w= Width of fly wheel
ρ= Density of the fly wheel = 7850kg/m
3
PARAMETERS:
Diameter of disc = 250mm
Diameter of shaft =25mm
Width of disc = 50mm
Density of plate= 7850kg/m
3


Procedure
1. Take the load hanger and pulling cord and hook the end loop over the peg on the
flywheel shaft.
2. Wind up a definite number of turns, say 8, from the position where the cord loop falls off
the peg.
3. Wind up the pulling cord 8 turns and hold the flywheel with one hand and a stop watch
with the other. The engraved mark should be by the pointer at this stage. Release the
flywheel and start the watch. Count the revolutions with the aid of the mark, using this to
judge when to stop the watches the set number of revolutions is turned. The load hanger
will fall on to the ground.
4. Repeat the above procedure adding loads by increment of 1Ν. Keep on repeating the
experiment until at least six readings have been obtained.
5. Try retiming one or two of the loads to see what the probable accuracy of the
measurement is.

4. MOMENT OF INTERTIA OF AFLYWHEEL.

DIAGRAM


RESULTS
Table 1
Acceleration of a flywheel
s/no No. of turns
Ν
Weight (mg) Time (t) s 1/t² Effective
couple
(Nm)
1. 10 0.5 51.0 0.00038
-0.1375
2. 10 1.0 32.0 0.00098 -0.0125

3. 10 1.5 25.0 0.00160 0.1125

4. 10 2.0 21.0 0.00227 0.2375

5. 10 2.5 19.0 0.00277
0.3625
6. 10 3.0 17.0 0.00346
0.4875
7. 10 3.5 16.0 0.00391 0.6125

5. MOMENT OF INTERTIA OF AFLYWHEEL.


GRAPH ANALYSIS










CALCULATION
CALCULATION OF EFFECTIVE COUPLE.
According to the graph, y-intercept = -1.059
1. 0.05 - 1.5286 =-1.4786*0.25=-0.3697
2. 0.55 - 1.5286 =0.9786*0.25=-0.2447
3. 1.55 - 1.5286 =0.0214*0.25=0.00535
4. 2.55 - 1.5286 =1.044*0.25=0.2554
5. 3.55 - 1.5286 =2.0214*0.25=0.5034
6. 4.55 - 1.5286 =3.044*0.25=0.7554
7. 5.55 - 1.8286 =4.0214*0.25=1.0054
Theoretical calculation of inertia of flywheel is given by;
K=I=ρπ??????
2
�
°
??????
2
2
= 7850 * π * 0.25
2
*0.030 *0.025
2
/2
=0.01445

6. MOMENT OF INTERTIA OF AFLYWHEEL.

Sources of errors
1.Human errors as the experiment was handled by human measurement instead of machines.
2.Miscalculation and inaccurate counting of the number of rotations.
3.High angular velocity of the wheel rotation.
4.Error in recording the time taken for the desired number of complete revolutions.
5.Energy loss by the apparatus to environment due to friction between the flywheel core and the
cord.

Conclusion
From the experiment, the moment of inertia of flywheel had been studied in which the results are
in the dependency of mass and radius of the wheel.
The experimental values of moment of inertia are found to have huge deviations from the
theoretical one.
The huge deviation is due to sources of errors and the decrease in the efficiency ratio of the
machine in the practical process.
We concluded that the error was done by human mistakes and also might be because of energy
loss due to friction. Thus, it is incomparable with the theoretical one because
REFERENCES
1. Egerton university, industrial and energy engineering department laboratory manual.
2. Bevan T. 1985 "Theory of Machines,"3
rd
Edition; CBS publishers, Delhi, India.
3. Khurmi, R. 2005 "Theory of Machines," 4
th
Edition, S. Chard publishers, New Delhi.
4. Ferd Beer and Russ Johnstone (2005) Vector Mechanics For Engineers; Statics, New Jersey,
McGraw-Hill
5. J.L. Meriam, L.G. Kraige (1998), Engineering Mechanics: Static SI Version, New York, John
Wiley & Sons Inc.
6. R.A. Serway, R. J. Beichner (2000), Physics: For Scientists and Engineers with Modern Physics,
Fifth Edition, Philadelphia, Saunders College Publishing
7. Anthony Bedford, Wallace Fowler, Kenneth M, Liechti, Bedford A. (2003),Statics and mechanics
of materials, Upper Saddle River, New Jersey, Prentice Hall.

7. MOMENT OF INTERTIA OF AFLYWHEEL.