Experiment # 14

To find the moment of inertia of flywheel.

Objective: To calculate the moment of inertia of flywheel.

Theoretical Background:

Moment of inertia:

It is a property of a body due to which body resists to bending moment.It depends on shape of body. It does not depend on the material of body. It is represented by “I”.Let “m” be the mass of wheel & “h” be the height from ground. Let wheel starts moving from rest i-e vi = 0

s = vav ts = (vi + vf)t/2s = (vf)t/2vf = 2s/t

Potential energy at height “h” isP.E = mgh

Kinetic energy, K.E = (mv2)/2Rotational K.E = K.Erot = (Iw2)/2

According to law of conservation of energyP.E = K.E + K.Erot

mgh = (mv2)/2 + (Iw2)/22mgh = mv2 + Iw2

I = (2mgh - mv2)/w2

Where w = v/r (r is radius & v is velocity of wheel)

& h = h1 – h2

Procedure:

First adjust the apparatus at certain height from the measure height from ground level to weight pan with the help of measuring tap.Now put the weights “m” in weight pan by keeping the wheel stationary. By using stick, start the stop watch & measure the time upto which the weight pan strikes the grond.Note that time by using this calculation, moment of inertia is found.Repeat the procedure for various loads and heights.

Observation and calculations:

R=0.5/12=0.042 ft

S.No

Mass (w/g)

Height H(ft)

Time t(sec)

V=2H/R W=v/r Inertia I=(2mgh - mv2)/w2

1 0.10 2 14.25 0.28 6.66 0.292 0.13 2 12.9 0.30 7.14 0.323 0.13 3 16.25 0.36 8.57 0.344 0.19 3 11.78 0.50 11.9 0.255 0.13 4 15.03 0.53 12.61 0.216 0.10 3 15.81 0.37 8.80 0.24

Data analysis: