Experiment # 02

To find the moment of inertia of flywheel

By falling weight method

Objective#

To calculate the moment of inertia of flywheel.

Apparatus used#

Fly wheel apparatus

Stop watch

Rope

Scale

Theoretical Background#

Fly wheel#

A heavy revolving wheel in a machine which is used

to increase the machine’s momentum and thereby

provide greater stability or a reserve of available

power.

Scale#

Scale is used for measuring the change in length and

also the length of inclined plane

Stop watch#

Stop watch is used to note a time.

Moment of inertia#

“The resistance to rotational or circular motion is

called

moment of inertia”

It depends on mass and radius of body. It is

represented by “I”.

Let “L” be the length of the inclined plane and “m” be

the mass of wheel.

s = vav t

let vi = 0

s = (vi + vf)t/2

s = (vf)t/2

vf = 2s/t

Potential energy at height “h” is

P.E = mgh

Kinetic energy, K.E = (mv2

)/2

Rotational K.E = K.Erot = (Iw2

)/2

According to law of conservation of energy

P.E = K.E + K.Erot

mgh = (mv2

)/2 + (Iw2

)/2

2mgh = mv2

+ Iw2

I = (2mgh – mv2

)/w2

Where

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

Experimental Procedure#

First of all we adjust the apparatus, at a height (h) we

adjust the hanger at a desired height.

After that a weight of certain value is put on it and

allowed it to move down the point at which it touches

the earth will be noted with the help of stop watch.

The values which we put into the formulae of

moment off inertia gives desired value.

This procedure is repeated for various loads and

heights.

Observation and calculations#

R=0.5 inch

R=0.5/12=0.042 f

Table

S. No m r H t V=2H/t ω=V/r I

1. 0.318 lb. 0.041 ft. 3.583 ft. 8 sec 0.895 ft/sec2

21.48 rad/sec 0.258 lb.ft2

2. 0.131 lb. 0.041 ft. 3.437 ft. 20 sec 0.343 ft/sec2

8.232 rad/sec 0.261 lb.ft2

3. 0.069 lb. 0.041 ft. 2.333 ft. 22 sec 0.212 ft/sec2

5.088 rad/sec 0.254 lb.ft2

4. 0.1 lb. 0.041 ft. 3.333 ft. 17 sec 0.392 ft/sec2

9.408 rad/sec 0.257 lb.ft2

5. 0.194 lb. 0.041 ft. 3.541 ft. 11.5 sec 0.615 ft/sec2

14.76 rad/sec 0.267 lb.ft2

6. 0.16 lb. 0.041 ft. 3.667 ft. 14 sec 0.523 ft/sec2

12.552 rad/sec 0.2601 lb.ft2

7. 0.22 lb. 0.041 ft. 4.166 ft. 12.5 sec 0.666 ft/sec2

15.984 rad/sec 0.249 lb.ft2

8. 0.1 lb. 0.041 ft. 3.041 ft. 15.5 sec 0.392 ft/sec2

9.408 rad/sec 0.269 lb.ft2