Compound pendulum

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:

Compound pendulum is defined as a right body suspended in a vertical plane, from a point on the body other than centre of gravity. On giving small angular displacements, it oscillates and perform harmonic motion.A compound pendulum has an extended mass, like a swinging bar, and is free to oscillate about a horizontal axis. A special reversible compound pendulum called Kater's pendulum is designed to measure the value of g, the acceleration of gravity.

Procedure:

1. Suspend the pendulum in the first hole by choosing the length 5 cm on the length slider.
2. Click on the lower end of the pendulum, drag it to one side through a small angle and release it. The pendulum will begin to oscillate from side to side.
3. Repeat the process by suspending the pendulum from the remaining holes by choosing the corresponding lengths on the length slider.
4. Draw a graph by plotting distance d along the X-axis and time period T along the Y-axis.
5. Calculate the average value of l/T2 for the various choices of T, and then calculate g as in step 2 above.
6. Determine kG and IG as outlined in steps 3 and 4 above.
7. Repeat the experiment in different gravitational environments by selecting an environment from the drop-down environment menu. If the pendulum has been oscillating, press the Stop button to activate the environment menu.

Observation Table:

Sr.no	b	T	t=T/10	I=(t2mgb)/4π	Ig=I-mb2
1	0.3	14.81	1.48	0.22	0.10
2	0.35	14.3	1.43	0.25	0.08
3	0.25	14.9	1.49	0.18	0.09
4	0.2	15.3	1.53	0.15	0.10

Results:

Moment of inertia of the compound pendulum (experimental) =0.09
Moment of inertia of the compound pendulum (analytical) =0.11