3. Aim: To find the moment of inertia of a flywheel.
Apparatus/Components:Fly wheel, weight hanger, slotted weights, stop watch, metre
scale.
Applications:
• Flywheels can be used to store energy and used to produce very high electric
power pulses for experiments, where drawing the power from the public electric
network would produce unacceptable spikes.
• Flywheels are used in punching machines and riveting machines. For internal
combustion engine applications, the flywheel is a heavy wheel mounted on the
crankshaft. The main function of a flywheel is to maintain a near constant angular
velocity of the crankshaft.
• The phenomenon of precession has to be considered when using flywheels in
moving vehicles.
Objectives:To determine the moment of inertia of a flywheel.
4. Theory/Concepts/Formulas (If Applicable)
The flywheel consists of a heavy circular disc/massive wheel fitted with a strong axle
projecting on either side. The axle is mounted on ball bearings on two fixed
supports. There is a small peg on the axle. One end of a cord is loosely looped
around the peg and its other end carries the weight-hanger.
Let "m" be the mass of the weight hanger and hanging rings (weight
assembly).When the mass "m" descends through a height "h", the loss in potential
energy is
Ploss= mgh
The resulting gain of kinetic energy in the rotating flywheel assembly (flywheel and
axle) is
Kflywheel=1/2 Iω2
Where , I -moment of inertia of the flywheel assembly
ω-angular velocity at the instant the weight assembly touches the ground.
5. Theory/Concepts/Formulas (If Applicable)
The gain of kinetic energy in the descending weight assembly is,
Kweight=1/2 mv2
Where v is the velocity at the instant the weight assembly touches the ground.
The work done in overcoming the friction of the bearings supporting the flywheel
assembly is
Wfriction=nWf
Where
n - number of times the cord is wrapped around the axle
Wf - work done to overcome the frictional torque in rotating the flywheel assembly
completely once
Therefore from the law of conservation of energy we get
Ploss=Kflywheel+Kweight+Wfriction ------------(1)
6. Theory/Concepts/Formulas (If Applicable)
On substituting the values we get
Now the kinetic energy of the flywheel assembly is expended in rotating N times
against the same frictional torque. Therefore
If r is the radius of the axle, then velocity v of the weight assembly is related to r by the
equation
V=ωr
Substituting the values of v and Wf we get:
7. Theory/Concepts/Formulas (If Applicable)
Now solving the above equation for I
Where, I = Moment of inertia of the flywheel assembly
N = Number of rotation of the flywheel before it stopped
m = mass of the rings
n = Number of windings of the string on the axle
g = Acceleration due to gravity of the environment.
h = Height of the weight assembly from the ground.
r = Radius of the axle.
Now we begin to count the number of rotations, N until the flywheel stops and also
note the duration of time t for N rotation. Therefore we can calculate the average
angular velocity ωaverage in radians per second
9. Procedure
•The length of the cord is carefully adjusted, so that when the weight-hanger just
touches the ground , the loop slips off the peg.
•A suitable weight is placed in the weight hanger
•A chalk mark is made on the rim so that it is against the pointer when the weight
hanger just touches the ground.
•The other end of the cord is loosely looped around the peg keeping the weight
hanger just touching the ground.
•The flywheel is given a suitable number (n) of rotation so that the cord is wound
round the axle without overlapping.
•The height (h) of the weight hanger from the ground is measured.
•The flywheel is released.
10. Procedure
•The weight hanger descends and the flywheel rotates.
•The cord slips off from the peg when the weight hanger just touches the ground.
By this time the flywheel would have made n rotations.
•A stop clock is started just when the weight hanger touches the ground.
•The time taken by the flywheel to come to a stop is determined as t seconds.
•The number of rotations (N) made by the flywheel during this interval is counted.
•The experiment is repeated by changing the value of n and m.
•From these values the moment of inertia of the flywheel is calculated using
equation
I=
𝑵𝒎
𝑵+𝒏
𝟐𝒈𝒉
𝝎𝟐 − 𝒓𝟐
11. Observations :
Mass
suspended
(m) x m-3
kg
Height
above
the
ground
(h) x 10-2
m
No. of
revolutions
before the
mass is
detached
(n)
No. of
revolutions
after the
mass is
detached
(N)
Time for
revolution
(t) s
Mean
angular
velocity
ω=
𝟒𝝅𝑵
𝒕
Moment
of Inertia
of
flywheel
(kgm2)
Mean value of moment of inertia, I =.........kgm2
Result : Moment of inertia of the fly wheel =.........kgm2
