Лабораторные работы / Решенная лабораторная по физике 05

The laboratory work N^o 5.

Determination of the moment of inertia by a method of oscillations.

Had done by the student gr: 220473я F.N.S. Pavlov F.E.

Checked by ______________________ date ____________

Purpose: to define the moment of inertial of monolithic core in respect of two parallel axes. The result to compare with the Schteiner’s theorem.

The order of performing a work:

1. To hang up a core on the threads strictly horizontal, by arranging it between directing.

2. To undertake for right directing and to turn a core on 4. Then sharply to unwrap a directing rod from a core, by giving it an opportunity to make oscillations in respect of axis (figure 1).

3. To measure the time of full oscillations (=10). To evaluate the period of oscillations (9 times). Then to evaluate <>.

4. To measure - distance between the points A and B for which suspended the core; - length of the threads.

5. To hang up a core for the end A and to produce oscillations in a vertical plane. The angle of a rejection doesn't to exceed 4.

6. To measure the times of full 10 oscillations of the core and evaluate (9 times). Then to evaluate <>.

7. Under the formulas , to evaluate

8. The casual rejections are equal: , ; a square rejections: , . The errors of results are: , .

9. The attitude and absolute errors to evaluate by formulas: ; .

10. ; .

11. To evaluate and .

12. To write data of measurements and calculations in the table 1-5.

Figure 1. Figure 2. Figure 3.

The lows of conservation of energy:

(1)

The core which is hang up on the two threads to make a harmonicall oscillations (figure 1). To define its max angular velocity , differentiating by the time:

(2)

The maximum height elevation of the center of masses is defining by the angel (figure 2):

At a little meanings of and the end of the core passes a way , which is approximately equal the length of the arch :

Then (3)

Using all formulas (1), (2) and (3) we have:

.

In to the formula (1) substitute a maximum meaning of velocity at passes the static state from (2) and the maximum height rise of the center of masses (figure 3). We have:

(4)

From the equation (1) with (2) and (4) we have:

.

Table N^o1.

, s	, s		, s	, s		, s
10	8,4		0,84	0,064		0,004096
	8,32		0,832	0,056		0,003136
	7,3		0,73	0,046		0,002116
	7,4		0,74	0,036		0,001296
	7,74		0,774	0,002		0,000004
	7,38		0,738	0,038		0,001444
	7,6		0,76	0,016		0,000256
	8,04		0,804	0,028		0,000784
	7,64		0,764	0,012		0,000144
<>=0,776		2,469			0,823

Table N^o2.

, s	, s		, s	, s		, s
10	8,1		0,81	0,027		0,000729
	7,5		0,75	0,033		0,001089
	7,62		0,762	0,021		0,000441
	8,06		0,806	0,023		0,000529
	7,49		0,749	0,034		0,001156
	8,08		0,808	0,025		0,000625
	8,04		0,804	0,021		0,000441
	7,47		0,747	0,036		0,001296
	8,07		0,807	0,024		0,000576
<>=0,783		2,49			0,83

Table N^o3.

kg	kg	m	m	m	m
0.0554	0.00005	0.24	0.005	0.42	0.005

Table N^o4.

				,	,
0.000290	0,00000061	0.001035	0,00000219	0.000745	0.000797

Table N^o5.

, %	%
2.11	2.12

Conclusion: so we have studied to define the moment of inertia of monolithic core in respect of two parallel axes.And to compare with the Schteiner’s theorem.

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