Work procedure and data processing

1. Determination of inertia moment of pendulum without loads.

1.1. Remove loads from the rods.

1.2. Fix the falling load at the level of the upper score marked on the plant.

1.3. Let the load go down and measure the time of its falling down to the lower score with a stop watch.

1.4. Repeat measurement 5 times and enter the results into table 5.4.

1.5. Calculate the magnitude of inertia moment for each experiment (using formula 5.8) and its average value. The values of pulley radius, height of falling and load mass are indicated in the passport of the work.

2. Determination of the total inertia moment of a pendulum with loads.

2.1. Fix the loads on every rod at the first score near the pulley.

2.2. Measure the distance l between the centre of loads and the centre of rotation with the help of a ruler. Enter the result into table 5.4.

2.3. Measure the time of load fall 5 times; enter the results into the table.

2.4. Fix loads on a medial, and then on farthest scores of the rods and execute actions suggested in items 2.2., 2.3.

2.5. Calculate the fractional error of the inertia moments measurement using formula 5.9. Calculate the absolute error of inertia moments by formula 5.10. Write down the results of indirect measurement of the pendulum moment of inertia without loads I₀ and with loads I’. Express results in SІ.

I₀ = I₀ ± І₀; I₁’ = I₁’ ± І₁’; I₂’ = I₂’ ± І₂’; I₃’ = I₃’ ± І₃’;

3. Determination of the loads inertia moment.

Calculate inertia moments of the loads placed in the first, second and third positions. Inertia moment of loads is calculated as the difference of the total inertia moment of pendulum with loads I’ and the inertia moment of pendulum without loads I₀:

; ; .

4. Plotting loads inertia moment dependence upon the distance of loads to the rotation centre.

4.1. Plot the graph as the dependence of loads inertia moment upon the square of loads distance to the rotation centre I = f (l²). Analyze the obtained graph.

Table 5.4

Loads position l, cm	Exp. No.	Load falling down time t, s	Average value , s	Random deviation ti, s	Root-mean square error Sn, s
Without loads	1 2 3 4 5
First position l1 =	1 2 3 4 5
Second position l2 =	1 2 3 4 5
Third position l3 =	1 2 3 4 5

Self-examination questions

1. What kinematical and dynamic characteristics is rotational motion described by?

2. What are the equations applied for determination of inertia moment of material point and the objects of regular geometrical form?

3. Write formulas of basic dynamics law for translational and rotary motion.

4. Deduce the expression for calculation of inertia moment in the lab.

5. Write Steiner’s theorem and explain its application.

6. What kind of dependence must be obtained in the work?