CN107680450A - A kind of Moment of Inertia Using Three-line Pendulum Method instrument - Google Patents
A kind of Moment of Inertia Using Three-line Pendulum Method instrument Download PDFInfo
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- CN107680450A CN107680450A CN201710967354.7A CN201710967354A CN107680450A CN 107680450 A CN107680450 A CN 107680450A CN 201710967354 A CN201710967354 A CN 201710967354A CN 107680450 A CN107680450 A CN 107680450A
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- lower disc
- line pendulum
- inertia
- moment
- upper bracket
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- G—PHYSICS
- G09—EDUCATION; CRYPTOGRAPHY; DISPLAY; ADVERTISING; SEALS
- G09B—EDUCATIONAL OR DEMONSTRATION APPLIANCES; APPLIANCES FOR TEACHING, OR COMMUNICATING WITH, THE BLIND, DEAF OR MUTE; MODELS; PLANETARIA; GLOBES; MAPS; DIAGRAMS
- G09B23/00—Models for scientific, medical, or mathematical purposes, e.g. full-sized devices for demonstration purposes
- G09B23/06—Models for scientific, medical, or mathematical purposes, e.g. full-sized devices for demonstration purposes for physics
- G09B23/08—Models for scientific, medical, or mathematical purposes, e.g. full-sized devices for demonstration purposes for physics for statics or dynamics
- G09B23/10—Models for scientific, medical, or mathematical purposes, e.g. full-sized devices for demonstration purposes for physics for statics or dynamics of solid bodies
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Abstract
The invention belongs to experimental instrument technology, discloses a kind of Moment of Inertia Using Three-line Pendulum Method instrument, including support, three-line pendulum, and three-line pendulum is made up of the suspension wire of upper disk, lower disc and three equal lengths of the upper disk of connection and lower disc；Base is connected with upper bracket by three vertical rods, and the rotary shaft of upper disk is vertically fixed on the crossbeam of upper bracket so that device is stable；The center of upper bracket is connected by connecting shaft with roll and jackscrew；Suspension wire one end and coiling axis connection, the other end are connected with lower disc, convenient to adjust three-line pendulum pendulum length, avoid rocking in three-line pendulum swing process.One fixed pointer of floor installation, a circumferential angle scale strip is carved with the circumferential edge of lower disc, angle spends groove mark from 0 to 360, precision is 0.1 degree, adjustment pointer is parallel to each other with scale strip graduation mark, when rotating lower disc, angular values of the pointer through scaleover can be observed, realize that accurate control rotational angle is less than 5 degree.
Description
Technical field
The invention belongs to experimental instrument technology, more particularly to a kind of Moment of Inertia Using Three-line Pendulum Method instrument.
Background technology
Rotary inertia is a basic physical quantity in rational mechanics, its value depend on the shape of object, Mass Distribution with
And the position of selected rotating shaft.For geometry is simple, the uniform rigid body of Mass Distribution, its phase directly can be calculated with formula
For the rotary inertia of a certain determination rotating shaft, but for complex contour and the object of non-uniform mass, experiment can only be passed through
Method accurately determines its rotary inertia.Therefore, experimental method carrys out Measuring Moment of Inertia Using and seems even more important.Three cycloid methods
It is the important method for measuring object rotation inertia, there is image clearly, easy to operation, suitable variously-shaped.One
Since straight, three-line pendulum measurement object rotation inertia experiment is most common experimental project in science and engineering Physical Experiment.But three lines
Arrangement exist because experimental provision and manual operation cause experimental error the drawbacks of.How to reduce experimental error is always each side's research
Object, prior art one：The derivation of solid moment of inertia measure equation and approximation method used are analyzed, and it is various near
Like the influence to experimental measurements；Prior art two：During three-line pendulum Measuring Moment of Inertia Using formula is derived, obtain
Go out rotary inertia error be mainly derived from swing maximum angular displacement it is excessive and operation in measure all numbers, rock and length survey
Amount error；
In summary, the problem of prior art is present be：Prior art is excessive for pivot angle, swings too high, cycle timing
Inaccurate, the factor such as swing process Instrumental is unstable, pivot angle twisting, cycloid regulation inconvenience does not solve disposably.
The content of the invention
The problem of existing for prior art, the invention provides a kind of Moment of Inertia Using Three-line Pendulum Method instrument.
The present invention is achieved in that a kind of Moment of Inertia Using Three-line Pendulum Method instrument, and the Moment of Inertia Using Three-line Pendulum Method instrument is provided with：
Upper bracket；
Three lines being made up of the suspension wire of upper disk, lower disc and three equal lengths of the upper disk of connection and lower disc
Pendulum；
The rotating shaft of the upper disc centre is vertically fixed on the crossbeam of the upper bracket；
The center of the upper bracket is connected by connecting shaft with roll and jackscrew.
Further, bottom plate is connected by three vertical rods with upper bracket.
Further, the bottom edge fixes a pointer by screw.
Further, circumferential angle graduation mark is carved with the circumferential edge on the lower disc surface, angle spends groove from 0 to 360
Mark, graduating accuracy are 0.1 degree.
The present invention is connected in the base of existing three-line pendulum rotational inertia analyzer with upper bracket by three vertical rods, upper disk
Rotary shaft be vertically fixed on the crossbeam of upper bracket so that device is stable；The center of upper bracket by connecting shaft with around
Bobbin and jackscrew connection；Suspension wire one end and coiling axis connection, the other end are connected with lower disc, convenient to adjust three-line pendulum pendulum length, are kept away
Rocking in three-line pendulum swing process is exempted from.One fixed pointer of floor installation, is carved with one in the circumferential edge of lower disc
Circumferential angle scale strip, angle spend groove mark from 0 to 360, and precision is 0.1 degree, adjusts pointer and scale strip graduation mark is mutual
It is parallel, when rotating lower disc, angular values of the pointer through scaleover can be observed, realize that accurate control rotational angle is less than 5 degree.
Brief description of the drawings
Fig. 1 is Moment of Inertia Using Three-line Pendulum Method instrument structural representation provided in an embodiment of the present invention；
Fig. 2 is disk rotational process schematic provided in an embodiment of the present invention；
In figure：1st, upper disk；2nd, lower disc；3rd, suspension wire；4th, bottom plate；5th, vertical rod；6th, upper bracket；7th, crossbeam；8th, roll；
9th, jackscrew；10th, pointer.
Embodiment
In order to make the purpose , technical scheme and advantage of the present invention be clearer, with reference to embodiments, to the present invention
It is further elaborated.It should be appreciated that the specific embodiments described herein are merely illustrative of the present invention, it is not used to
Limit the present invention.
The application principle of the present invention is explained in detail below in conjunction with the accompanying drawings.
As shown in figure 1, Moment of Inertia Using Three-line Pendulum Method instrument provided in an embodiment of the present invention includes：Upper disk 1, lower disc 2, suspension wire 3, bottom
Plate 4, vertical rod 5, upper bracket 6, crossbeam 7, roll 8, jackscrew 9, pointer 10.
Bottom plate 4 is connected by three vertical rods 5 with upper bracket 6, and the rotating shaft at the upper center of disk 1 is vertically fixed on upper bracket 6
On crossbeam 7, the center of the upper frame of branch 6 is connected by connecting shaft with roll 8, jackscrew 9；The edge of bottom plate 4 is fixed by screw
One pointer 10, circumferential angle graduation mark being carved with the circumferential edge on the surface of lower disc 2, angle spends groove mark from 0 to 360,
Graduating accuracy is 0.1 degree.
Adjustment pointer 10 is parallel to each other with scale strip graduation mark, and when rotating lower disc 2, pointer 10 can be observed through scaleover
Angular values, realize that accurate control rotational angle is less than 5 degree.
The application effect of the present invention is explained in detail with reference to experiment.
The angular speed of lower disc rotation process is that ω, h are lower disc because of the height that suspension wire reverses and rises, θ in Fig. 20For
Angular amplitude, T are vibration period, J0For rotary inertia of the lower disc to upper lower burrs central axis, ω0During to return to equilbrium position
Angular speed.
When lower disc returns to equilbrium position, kinetic energy Ek=1/2J0ω0 2, increased potential energy E during peakr=mgh.Ignore
Air drag and frictional resistance, 1/2J is had according to the law of conservation of mechanical energy0ω0 2=mgh.From lower disc angular displacement with time t's
Relation can derive that the relation of angular velocity omega and time t is：
θ=θ0sin2π t/T, ω=d θ/dt=2 π θ0/T·cos2πt/T；
Work as t=0, when T/2, T, 3T/2 ..., lower disc passes through equilbrium position, ω0=ωmax=2 π θ0/ T, therefore：
Mgh=1/2J0(2πθ0/T)2；
When pivot angle amplitude is θ0When, certain suspension point A is moved to position A on lower disc1, the lifting height of disc shaft is：
H=loo1=lBC-lBC1=(lBC 2-lBC1 2)/(lBC+lBC1)；
L in formulaOO1、lBC、lBC1It is O and O1, B and C, B and C1The distance between, analysis can obtain：
H=2Rr (1-cos θ0)/lBC=4Rrsin2θ0/2/(2H–h)；
Due to H>>H, so 2H-h ≈ 2H, pivot angle θ0During very little, sin2θ0/2≈(θ0/2)2≈θ0 2/ 4, therefore：
H=Rr θ0 2/2H；
Therefore, can obtain：
J0=mgRrT0 2/4π2H；
By using Moment of Inertia Using Three-line Pendulum Method instrument of the present invention, experiment measurement accuracy can be improved well, and realizes three-line pendulum reality
Test measurement of the instrument to actual object rotary inertia.
The foregoing is merely illustrative of the preferred embodiments of the present invention, is not intended to limit the invention, all essences in the present invention
All any modification, equivalent and improvement made within refreshing and principle etc., should be included in the scope of the protection.
Claims (4)
1. a kind of Moment of Inertia Using Three-line Pendulum Method instrument, it is characterised in that the Moment of Inertia Using Three-line Pendulum Method instrument is provided with：
Upper bracket；
The three-line pendulum being made up of the suspension wire of upper disk, lower disc and three equal lengths of the upper disk of connection and lower disc；
The rotating shaft of the upper disc centre is vertically fixed on the crossbeam of the upper bracket；
The center of the upper bracket is connected by connecting shaft with roll and jackscrew.
2. Moment of Inertia Using Three-line Pendulum Method instrument as claimed in claim 1, it is characterised in that bottom plate is connected by three vertical rods with upper bracket.
3. Moment of Inertia Using Three-line Pendulum Method instrument as claimed in claim 2, it is characterised in that the bottom edge fixes a finger by screw
Pin.
4. Moment of Inertia Using Three-line Pendulum Method instrument as claimed in claim 1, it is characterised in that be carved with circle in the circumferential edge on the lower disc surface
All angle graduation marks, angle spend groove mark from 0 to 360, and graduating accuracy is 0.1 degree.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201710967354.7A CN107680450A (en) | 2017-10-17 | 2017-10-17 | A kind of Moment of Inertia Using Three-line Pendulum Method instrument |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201710967354.7A CN107680450A (en) | 2017-10-17 | 2017-10-17 | A kind of Moment of Inertia Using Three-line Pendulum Method instrument |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CN107680450A true CN107680450A (en) | 2018-02-09 |
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| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201710967354.7A Pending CN107680450A (en) | 2017-10-17 | 2017-10-17 | A kind of Moment of Inertia Using Three-line Pendulum Method instrument |
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Citations (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN202770589U (en) * | 2012-07-17 | 2013-03-06 | 东华大学 | Rotational inertia measuring instrument of three-line pendulum |
| CN106373463A (en) * | 2016-11-01 | 2017-02-01 | 江南大学 | Experiment instrument for three-line pendulum |
| CN106448362A (en) * | 2016-10-18 | 2017-02-22 | 江南大学 | Three-line pendulum facilitating control of pendulum angle |
| CN107036760A (en) * | 2017-06-13 | 2017-08-11 | 安徽新华学院 | A kind of three-line pendulum solid moment of inertia measures experimental rig |
| CN206546234U (en) * | 2017-03-01 | 2017-10-10 | 江南大学 | Easily adjust disk on three-line pendulum |
| CN207663632U (en) * | 2017-10-17 | 2018-07-27 | 西安电子科技大学 | A kind of Moment of Inertia Using Three-line Pendulum Method instrument |
-
2017
- 2017-10-17 CN CN201710967354.7A patent/CN107680450A/en active Pending
Patent Citations (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN202770589U (en) * | 2012-07-17 | 2013-03-06 | 东华大学 | Rotational inertia measuring instrument of three-line pendulum |
| CN106448362A (en) * | 2016-10-18 | 2017-02-22 | 江南大学 | Three-line pendulum facilitating control of pendulum angle |
| CN106373463A (en) * | 2016-11-01 | 2017-02-01 | 江南大学 | Experiment instrument for three-line pendulum |
| CN206546234U (en) * | 2017-03-01 | 2017-10-10 | 江南大学 | Easily adjust disk on three-line pendulum |
| CN107036760A (en) * | 2017-06-13 | 2017-08-11 | 安徽新华学院 | A kind of three-line pendulum solid moment of inertia measures experimental rig |
| CN207663632U (en) * | 2017-10-17 | 2018-07-27 | 西安电子科技大学 | A kind of Moment of Inertia Using Three-line Pendulum Method instrument |
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