Experiment # 10

To find the moment of inertia of the wheel.

Objective:

To calculate the moment of inertia of wheel that rolls down on an inclined plane

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 “s” be the length of the inclined plane and “m” be the mass of wheel. Let wheel start 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

& h = h1 – h2

Procedure:

Place wheel on inclined plane. Take a stop watch at time of leaving wheel from upper end of inclined plane. Wheel starts rotating. When it just strikes other end of inclined plane, stop the stop watch & measure time “t”. By using this find the velocity of wheel. Then put these values in formula & the moment of inertia . Repeat the different heights of inclined plane & find the moment of inertia for these different values.

Observation and calculations:

Weight =w= 8.5lbm=0.264 kg

length=l=83.4 cm=2.74 ftradius of axle =r=.0208 ft

S.No. H1 H2 H=H1+H2 t(sec)

V=2l/t W=v/r I=(2mhg-mv2)/w2

1 0.540 0.37 0.17 14.8 0.37 17.78 0.0092 0.610 0.37 0.24 12 0.46 21.95 0.00853 0.47 0.37 0.1 19 0.29 13.87 0.00874 0.313 0.625 0.312 12.3 0.51 24.48 0.00875 0.301 0.5 0.187 14.6 0.37 17.81 0.0092

Average I =0.0088 slug-ft2

Data Analysis: