CN1003807B - Device and method for measuring moment of inertia of rigid bodies - Google Patents

Abstract

The present invention provides a device and a method for measuring the solid moment of inertia, which is especially suitable for measuring the moment of inertia of objects with uneven weight distribution and regular cross-sectional shapes. When an object supporting table carried with an object to be measured rotates in a horizontal direction, thin rods for shading at the lower part of the object supporting table pass through a photoelectric switch one by one. At the time, a signal is transmitted, the angular displacement, the angular speed, the angular acceleration, etc. of the object to be measured in rotation can be directly measured, and the moment of inertia can be obtained through calculation. Additionally, the device can also be used for verifying the rotating principle and the parallel axis theorem of solids. The device has the advantages of easy operation, small frictional moment and small measuring error (smaller than 2%), and can be used for college physics teaching experiments, engineering design, scientific research, etc.

Description

The measuring moment of inertia of rigid bodies device and method

The present invention is a kind of determinator and method of solid moment of inertia, is specially adapted to the moment of inertia of the even rigid body in irregular shape of quality measurement skewness.

As everyone knows, the moment of inertia of the object of all even section configuration rule of mass distribution is that available mathematical formulae calculating is tried to achieve, but then must could measure with special determinator the moment of inertia of non-uniform mass and the irregular object of section configuration.* this special permission discloses a kind of moment of inertia that clear 53-148487 introduces and determines device, be that testee is placed on the universal stage with horizontal rotating shaft, because testee and universal stage are around the rotating shaft rotation on vertical plane, will inevitably be subjected to the influence of self gravitation during rotation, if testee non-uniform mass or section configuration are irregular, its velocity of rotation will be sometimes fast and sometimes slow, even basic rotation is not got up.And it seems that from the structure of this determinator error at measurment is inevitable very big.In addition, this device is directly to measure the counterweight a certain height required time that descends, and promptly measures the linear velocity that counterweight descends earlier, is converted into behind the angular velocity again through repeatedly converting, and just can obtain moment of inertia.

The purpose of this invention is to provide a kind of novel processional moment measuring device and method, it has advantage easy and simple to handle, that measuring accuracy is high, and is specially adapted to measure the moment of inertia of non-uniform mass and the irregular object of section.

Device of the present invention mainly comprises: bearing table, cone pulley, rotating shaft, base, pulley, be that the fine rule of counterweight and the optoelectronic switch that is connected with digital millisecond counter are arranged.Testee is placed on the bearing table that level installs, and links to each other measured object, bearing table and rigid system of cone pulley formation with cone pulley below the bearing table.Cone pulley is made up of 5 to 8 reels that radius is different, and the rotating shaft in the cone pulley is vertical, and its upper and lower side adopts bearing to reduce friction.On the reel of fine rule one end in the cone pulley, there is counterweight in the other end system that strides across pulley.When rigid system rotates in the horizontal direction, lightproof thin bar under the bearing table also rotates thereupon together, during in succession by optoelectronic switch, signal is delivered to digital millisecond counter, measure testee and rotate the required time of a certain angle, can directly record angular displacement, and calculate angular velocity, angular acceleration, opplied moment, moment of friction, thus obtained moment of inertia.

It is as follows to utilize the present invention to measure the method for solid moment of inertia:

Measured object is positioned on the bearing table, selects a reel radius r, the counterweight quality is m, the binary channels millisecond meter is preset at measures rotational angle θ ₁And θ ₂On, when the counterweight free-falling, measure rotational angle θ simultaneously with the binary channels millisecond meter ₁And θ ₂The used time t in back ₁And t ₂After fine rule broke away from cone pulley, rigid system was only done to slow down under the moment of friction effect to rotate, and rotates θ when millisecond meter can be measured retarded motion ₁, θ ₂Used time t ₁', t ₂', the rotational motion equation is as follows:

θ ₁＝ω ₁t ₁+1/2β ${\mathrm{<figure-callout\; id="1"\; label="t"\; filenames="86106881\_DRIMG1.png,86106881\_DRIMG2.png"\; state="\{\{state\}\}">t</figure-callout>}}_{1^2}$ ①

θ ₂＝ω ₂t ₂+1/2β $t_{2^2}$ ②

ω in the following formula ₁, ω ₂Be respectively the initial angle speed of two lightproof thin bars.Because two lightproof thin bars are shading simultaneously for the first time, therefore

ω ₁＝ω ₂③

Can derive the formula of angular acceleration β by 1. and 2. formula:

$\mathrm{\beta =}\frac{{\mathrm{2(\theta }}_2{t}_2{\mathrm{-\theta }}_1{t}_2)}{t_{2^2}{t}_1{\mathrm{-<figure-callout\; id="1"\; label="t"\; filenames="86106881\_DRIMG1.png,86106881\_DRIMG2.png"\; state="\{\{state\}\}">t</figure-callout>}}_{1^2}{t}_2}$

④

Angular acceleration is β ' when slow down rotating, the t of formula in 4. ₁And t ₂Change into t ₁' and t ₂', just can obtain β '.

Again by law of rotation

mgr-Mμ＝βJ ⑤

-Mμ＝-β′J ⑥

Draw the formula of measuring moment of inertia:

J＝mgr/β+β′ ⑦

J is the moment of inertia of rigid system in the determinator in the following formula, and mgr is an opplied moment, and M μ is a moment of friction.Use the same method and measure its device moment of inertia Jo when unloaded, then the moment of inertia Jx of testee is:

Jx＝J-Jo

The present invention rotates in the horizontal direction owing to bearing table, even so measured object quality skewness or the irregular mensuration that does not also influence its moment of inertia of section configuration, broken away from from measuring the counterweight used time conversion of a certain height of falling and gone out these out-of-date methods of moment of inertia, thereby and replace the method that moment of inertia is tried to achieve in rotation the used time of a certain angle of measuring, and make these physical concepts clear and definite more, directly perceived, measure easy; Because bearing has all been adopted in rotating shaft up and down, reduced moment of friction, thereby improved measuring accuracy greatly simultaneously.The present invention can not only supply institution of higher education's physics teaching usefulness, can also be for the usefulness of engineering design and scientific research project measurement.

Embodiments of the invention describe by following accompanying drawing.

Fig. 1 is a measuring moment of inertia of rigid bodies apparatus structure synoptic diagram

Fig. 2 is the cone pulley cut-open view

Fig. 3 is the bearing table vertical view

Bearing table (1) is linked to each other by same rotating shaft (10) with cone pulley (3), is installed on the base (5).Three legs are arranged at base (5) bottom, and the horizontality of bearing table (1) is regulated in every leg bottom with set screw (6).Respectively there is a lightproof thin bar (2) bearing table (1) both sides, bottom, have framework (9) to be exclusively used on the base (5) symmetrical two optoelectronic switches (4) are installed, and optoelectronic switch (4) is connected with two-channel digital millisecond meter (not shown).Cone pulley (3) is made up of the reel of five different-diameters, and its diameter reduces from top to bottom gradually, goes up wheel diameter most and is about 7cm, descends wheel diameter to be about 3cm most.Fine rule one end can be as required on a certain reel, and the other end that it strides across pulley (7) can be selected the counterweight (8) of different quality as required for use.

Wheel shaft (10) upper end diameter is about 6mm, and lower end diameter is about 10mm, and radial ball bearing (11) is equipped with in the upper end, and thrust ball bearing (12) is equipped with in the lower end, and moment of friction is reduced to 10 ^-4Newton meter.

Bearing table (1) is a cruciform, and four arms are arranged.Three circular holes that distribute are symmetrically and evenly arranged on every arm, can put into little steel column in the circular hole, * is for the usefulness of checking parallel axis theorem.

Measuring error of the present invention (comparing with theoretical value) is in 2%.

Claims (4)

1, a kind of determinator of solid moment of inertia by bearing table, reel, base, pulley, time set, counterweight be to be made up of the fine rule of counterweight, is characterized in that:

Top and bottom in rotating shaft are equipped with transverse bearing and thrust bearing respectively; The bearing table across has four arms, and equally distributed circular hole more than three is arranged on every arm, the position of circular hole all on by the radial line at bearing table center in order to the little steel column of packing into, the checking parallel axis theorem; Cone pulley is made up of the different reel of several diameters, and diameter reduces from top to bottom gradually, and said time set is made up of optoelectronic switch (4) and two-channel digital millisecond meter.

Bearing table (1) is linked to each other by a rotating shaft (10) with cone pulley (3), be installed on the base (5), the horizontality of bearing table is regulated in three-legged bottom, the bottom of base (5) with set screw (6), respectively there is a lightproof thin bar (2) both sides, bottom of bearing table (1), symmetrical two optoelectronic switches (4) of the special-purpose installation of framework (9) are arranged on the base (5), optoelectronic switch (4) is connected with the two-channel digital millisecond meter, when lightproof thin bar rotates with bearing table, electronic switch by linking to each other in succession with digital millisecond counter, thus can directly measure the required time of angular displacement that turns over a certain special angle.

2, the determinator of a kind of solid moment of inertia according to claim 1 is characterized in that, cone pulley (3) is made up of the reel of five different-diameters, going up most wheel diameter is 7cm, descending most wheel diameter is 3cm, and wheel shaft (10) upper end diameter is 6mm, and lower end diameter is 10mm.

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