The checking of the theorem of Hagens and Steiner by using a rotational pendulum

Tema	Fizika
Tipas	Laboratorinis darbas
Aprašymas	Heigenso ir Steinerio teoremos tikrinimas sukamąja svyruokle. Darbas anglų kalba. Objective. Theory. Experimental and principal measurements. Data. Conclusion. References.
Patalpinta	2009-05-22
Parsisiuntė	44
	Parsisiųsti222 KB

Išsamus aprašymas

Objective. Our main task is to calculate the moment of inertia of the rotational pendulum by watching its period and to observe the change of the moment of inertia by changing the position of the weights which are on the beam. What is more, we shall experimentally check the principle of additivity for the moment of inertia of system of bodies, and also the theorem of Hagens and Steiner.
Equipment:
a) Rotational pendulum;
b) Two weights;

Theory. Moment of inertia, also called mass moment of inertia or the angular mass, (kg•m2) is a measure of an object's resistance to changes in its rotation rate. It depends on the mass of the rotational system and its distrubution with respect to Oz axis. We can calculate it using this formula:


The principle of additivity – the moment of inertia of a system consisting of several bodies is equal to the sum of moments of inertia of those bodies:


If we change the position of the axis with respect to the body, Iz will change too. Let us denote the moment of inertia of body, which is going through its centre of masses, with its mass m as Ic. Then, the moment of inertia of the same body but on the same axis, which is parallel to the first one and distant from it with the value ℓ, can be calculated using the theorem of Hagens and Steiner:


Experimental and principal measurements.

1. When we measure the length of the beam of pendulum l0, we calculate its moment of inertia I0, with respect to the axis which is passing through its centre of masses. Then we write the results into the table Nr. 1.

Raktiniai žodžiai

• hagens principle
• ginklo pendula
• our main task is to calculate the moment of inertia of the rotational pendulum by watching its period and to observe the change of the moment of inertia by changing