Aim:
To find the moment of inertia of the compound pendulum.
Apparatus:
A steel rod with holes in it for suspension (bar pendulum), A knife edged fulcrum, stop watch, meter scale
Theory:
A flywheel; is a heavy metal wheel attached to the shaft of the prime mover (motor or engine). Flywheels have most of their mass concentrated on the circumstances, thereby giving high moment of inertia. We know rotating bodies possess kinetic energy given by the relation K.E = 1 /2 Iω2 . Hence if moment of inertia I is increased, K.E also increases. Flywheels thus store the kinetic energy and release it back to the system when required. They are therefore called as ‘reservoir of energy’. An imported application of a flywheel is in a mechanical press where for a fraction of time high energy is required for actual punching, shearing or forming. This energy is supplied by the flywheel. During the longer non active period, the speed of the flywheel is built up slowly by a low powered motor. Thus the motor is not overloaded and also results in energy saving. In automobiles, the flywheel is provided by the combustion in the cylinders and provides energy for the compression stroke in the pistons.
Procedure:
- Wind a string around the shaft of the flywheel. Attach a pan of known weight from the end of the string. Hold the pan i.e. does not allow the flywheel to rotate.
- Measure the diameter of the axle with a vernier caliper
- . Add some weight in the pan and note the total mass ‘m’ of the pan. Also note the height ‘h’ of the base of the pan from the ground.
- Hold a stop watch and now release the pan. The pan accelerates and gains velocity as it travels down. Note the time and rotations ‘N1’ turned by the flywheel till the pan touches the ground.
- When the pan hits the ground it gets detached from the flywheel. The flywheel continues to rotate. Note the rotations ‘N2’ turned by the flywheel from the moment the pan touches the ground till the flywheel stops.
- Repeat the above steps by changing the height of the pan from the ground and the moment weight in the pan for one more set of observations.
Obsevation Table
| Sr No. | N | n | H | t | w | I |
|---|---|---|---|---|---|---|
| 1 | 12 | 6 | 1.23 | 23.24 | 3.24 | 0.35 |
| 2 | 9 | 5 | 1.17 | 18.74 | 3.35 | 0.3 |
| 3 | 6 | 4 | 1.1 | 13.41 | 3.79 | 0.23 |
Results:
Moment of inertia of the compound pendulum (experimental) = 0.3
Moment of inertia of the compound pendulum (analytical) = 0.35
Observation Table calculator
| So. No. | N | n | t | H | w | I |
|---|---|---|---|---|---|---|
| 1 | ||||||
| 2 | ||||||
| 3 |