LABORATORY WORK № 43.5

TORSION PENDULUM

Purpose of work is to study of laws of oscillations of the torsion pendulum.

Task: check up dependence of period of free oscillations torsion pendulum from its moment of inertia; check up a formula for the moment of inertia of ball (peg).

Devices and equipments: torsion pendulum, set of cylinders or pegs, balls.

Figure 14.1

The experimental setting (fig.14.1) consists of basis 1. In basis a peg is fastened 3, on what fix lower bracket 4 and overhead 13. On these brackets on a steel wire 16 the suspended scope 9, which has a moving slat 10 with two fixative nuts 11. In a scope on two centrings dowels 14 the probed body is fastened 15 (cylinder, peg, cube, ball) and it is compressed spirally 12. On a scope small flag is fastened 7, which, crossing the light ray of photoelectric sensor 8, includes the electronic system of count of amount oscillations (indicator 17) and stop-watch (indicator 22). After help of this small flag a scope of fix is in initial position of electromagnet 6 at certain corner of turn which is measured on a scale 5. On the front panel of device are: switches 18 – “Сеть'”, 19 – “Срос”, 20 “Пуск” 21 – “FEET”.

Theoretical part

A turning pendulum is a body, which can be revolved in relation to an arbitrary axis under the action of resilient force, which arises up during deformation of twisting of wire, which the fastened body is on. Write down the fundamental equation of the rotational motion dynamics

(14.1)

where I is a moment of inertia of body, is an angular acceleration. During deformation of twisting of wire the moment of force is proportional the corner of rollup, that

(14.2).

Figure 14.2

A sign does minus take into account, that the moment of force is diminished by the corner of turn α. Get differential equation of oscillations of the turning pendulum

. (14.3)

Comparing this equation to general equation of undamped harmonic oscillations

, (14.4)

get cyclic frequency and period of oscillation of the turning pendulum

. (14.5)

For implementation of the first point of task it is necessary to change the moment of inertia of pendulum. It is carried out replacement of bodies which are fastened in a scope 9. For this purpose the complete set of loads is used with different geometrical sizes, but with identical mass. A moment of inertia of cylinder is in relation to its axis

(14.18).

Moment of inertia of peg in relation to an axis, what perpendicular to it and passes through his middle

(14.8).

A moment of inertia of ball is in relation to a diameter

(14.9).

The substitution of this expressions in a formula (14.5), taking into account the moment of inertia of scope of I_p and additivity of moment of inertia, enables to calculate the periods of oscillations:

cylinder , (14.10)

peg , (14.11)

balls . (14.12)

Bringing expressions (14.10), (14.11) and (14.12) to the square, get:

~ R² (14.13)

~ L² (14.14)

~ R² (14.15)

From formulas (14.13) - (14.15) evidently, that the squares of periods of oscillations are proportional the squares of the proper characteristic geometrical sizes of bodies (radius, length).

Date: 2015-12-24; view: 815