CN217214003U - Experimental device for verifying conservation of angular momentum law - Google Patents
Experimental device for verifying conservation of angular momentum law Download PDFInfo
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- CN217214003U CN217214003U CN202220575038.1U CN202220575038U CN217214003U CN 217214003 U CN217214003 U CN 217214003U CN 202220575038 U CN202220575038 U CN 202220575038U CN 217214003 U CN217214003 U CN 217214003U
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Abstract
The utility model provides an experimental device for verify law of conservation of angular momentum, the purpose is solved among the prior art because of the coefficient of friction between objective table and the test piece is less, and the test piece can't reach the unchangeable steady state of relative position with the objective table in enough short time, leads to the influence of the friction moment on the main shaft to be ignorable, and then can not verify the technical problem of law of conservation of angular momentum. The experimental device comprises: the top of the object stage is provided with an anti-skidding structure, and the object stage can rotate; the light blocking rod is arranged on the objective table; a photoelectric gate couplable to the light barrier; and the counting timer is electrically connected with the photoelectric gate. The technical scheme has the advantages that the test piece and the object stage can reach a stable state with unchanged relative positions in a short enough time, so that the influence of friction moment on the main shaft can be ignored, and the law of conservation of angular momentum can be verified.
Description
Technical Field
The utility model relates to a physical experiment teaching device specifically relates to an experimental apparatus who verifies the law of conservation of angular momentum.
Background
The law of conservation of angular momentum means that the angular momentum of the system remains unchanged when the resultant external moment borne by the system is zero. The angular momentum is equal to the product of the rotational inertia and the angular velocity, and the rotational inertia and the angular velocity can be measured by using the rotational inertia experimental instrument, so that the rotational inertia experimental instrument has the main parameter measurement requirement for verifying the angular momentum conservation law.
To verify the law of conservation of angular momentum, firstly, the motion state of the system needs to be changed (the magnitudes of the rotational inertia and the angular velocity are changed), and the rotational inertia and the angular velocity of the system before and after the state is changed are respectively calculated; and secondly, before and after the motion state of the system is changed, the external torque is zero or can be ignored.
The condition is easier to satisfy, and the second condition is the key to verify the law of conservation of angular momentum by overcoming the friction torque which is not zero or can not be ignored.
The rotational inertia experimental instrument adopting a constant moment method in the prior art has the following problems: because the friction coefficient between the objective table and the test piece is small, the test piece cannot reach a stable state with unchanged relative position with the objective table in a short enough time, and the influence of the friction moment on the main shaft cannot be ignored, so that the law of conservation of angular momentum cannot be verified.
SUMMERY OF THE UTILITY MODEL
To among the prior art because of the coefficient of friction between objective table and the test piece is less, the test piece can't reach the unchangeable stable state of relative position with the objective table in enough short time, leads to the influence of friction moment on the main shaft to be ignorable, and then can not verify the technical problem of angular momentum conservation law, the utility model provides an it can reach the unchangeable stable state of relative position in enough short time to verify the experimental apparatus of angular momentum conservation law to have and make test piece and objective table, make the influence of friction moment on the main shaft negligible to verify the advantage of angular momentum conservation law.
The technical scheme of the utility model is that:
an experimental apparatus for verifying the law of conservation of angular momentum, comprising:
the top of the object stage is provided with an anti-skidding structure, and the object stage can rotate;
the light blocking rod is arranged on the objective table;
a photoelectric gate couplable to the light barrier;
and the counting timer is electrically connected with the photoelectric gate.
Optionally, the non-slip structure is a non-slip layer or a non-slip mat.
Optionally, two sides of the bottom of the object stage are respectively and symmetrically provided with one of the light blocking rods, and the photoelectric door is located below the object stage.
Optionally, the experimental apparatus further comprises:
the cone pulley is arranged at the bottom of the objective table;
one end of the pull rope is connected with the cone pulley;
the pull rope can be wound on the cone pulley and is connected with the objective table through the cone pulley.
Alternatively,
a plurality of wheel surfaces with uniformly increasing radiuses are arranged on the cone pulley along the axial direction of the cone pulley;
the pull rope can be detachably connected with the wheel surface of each cone pulley respectively and is wound on the corresponding wheel surface.
Optionally, the pulling ropes are densely wound on the wheel surface of the cone pulley in a non-overlapping mode.
Optionally, the experimental apparatus further comprises: and the power part is connected with one end of the pull rope, which is far away from the cone pulley.
Further, the power part comprises a plurality of weights.
Optionally, the experimental apparatus further comprises:
a base;
the bottom of the cone pulley is rotatably connected to the base, and the photoelectric door is located on the base.
Optionally, the experimental apparatus further comprises:
the fixed pulley is wound by the pull rope, one section of the pull rope between the fixed pulley and the cone pulley is in a horizontal shape, and the other section of the pull rope is in a vertical shape.
Compared with the prior art, the beneficial effects of the utility model are that:
in this technical scheme, set up anti-skidding structure through the top at the objective table, increase the frictional force between test piece and the objective table for when not placing on the objective table suddenly around main shaft pivoted test piece originally, the test piece can reach the unchangeable stable state of relative position with the objective table in enough short time, thereby make no relative gliding motion state between test piece and the objective table, and then make the influence of friction moment on the main shaft negligible, and then verify the law of conservation of angular momentum.
Drawings
In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present application, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.
Fig. 1 is a schematic structural diagram of the present invention.
Reference numerals:
1. a test piece; 2. an object stage; 3. a cone pulley; 4. a main shaft; 5. a base; 6. a light blocking rod; 7. a photogate; 8. a count timer; 9. a fixed pulley; 10. a weight; 11. pulling a rope; 12. a non-slip mat.
Detailed Description
In the following, only certain exemplary embodiments are briefly described. As those skilled in the art will recognize, the described embodiments may be modified in various different ways, all without departing from the spirit or scope of the present invention. Accordingly, the drawings and description are to be regarded as illustrative in nature, and not as restrictive.
Embodiments of the present invention will be described in detail below with reference to the accompanying drawings.
Example (b):
as shown in fig. 1, an experimental device for verifying the law of conservation of angular momentum comprises an object stage 2, a light blocking rod 6, a photoelectric door 7, a counting timer 8, an anti-skid pad 12, a pull rope 11, a weight 10 and a cone pulley 3. Specifically, the method comprises the following steps:
the objective table 2 is a circular table-shaped structure, the objective table 2 is provided with a central axis, and the objective table 2 can rotate around the central axis thereof, including uniform rotation, accelerated rotation or decelerated rotation. The top surface of the object table 2 is provided with an anti-slip structure, typically a non-slip mat 12 or layer. In the present technical solution, an anti-slip structure is taken as the anti-slip mat 12 as an example. Through setting up anti-skidding structure, frictional force between increase test piece 1 and objective table 2 when objective table 2 rotates with certain speed, places test piece 1 at the top of slipmat 12, and test piece 1 can reach the unchangeable steady state of relative position with objective table 2 in enough short time.
The bottom of objective table 2 is provided with a cone pulley 3, and the axis of cone pulley 3 and axis collineation when objective table 2 rotates, cone pulley 3 fixed connection is in the bottom of objective table 2, and cone pulley 3 rotates along with objective table 2. The wheel surface of the cone pulley 3 is detachably connected with a pull rope 11, one end of the pull rope 11 is connected to the wheel surface of the cone pulley 3, and the pull rope 11 can be wound on the wheel surface of the cone pulley 3. The other end of the pull rope 11 is provided with a power part for driving the pull rope 11, in the scheme, the power part is a weight 10, the weight 10 is hung at the end part of the pull rope 11, and the number of the weights 10 can be increased or decreased.
In the initial state (before verifying the conservation law of angular momentum), the pull rope 11 is wound on the cone pulley 3, and the weight 10 can move vertically downwards. The middle part of the pull rope 11 winds around a fixed pulley 9, one section of the pull rope 11, which is positioned between the fixed pulley 9 and the cone pulley 3, is in a horizontal state, and one section of the pull rope 11, which is positioned between the weight 10 and the fixed pulley 9, is in a vertical state. The direction of the force on the pulling rope 11 is changed by the fixed pulley 9, and the moment of inertia of the fixed pulley 9 is negligible.
Two opposite sides of the bottom of the object stage 2 are respectively provided with a light blocking rod 6, and the two light blocking rods 6 are symmetrically distributed about the central axis of the object stage 2. The photoelectric gate 7 is located below the stage 2, and a gap is provided between the photoelectric gate 7 and the bottom surface of the stage 2. When the object stage 2 rotates, the two light blocking rods 6 can sequentially pass through the photoelectric door 7, and the photoelectric door 7 can sense the number and time interval of the passing of the light blocking rods 6. The photoelectric gate 7 is electrically connected with the counting timer 8.
In the technical scheme, the friction torque of cone pulley 3 when rotating is very little, objective table 2 rotates together with cone pulley 3, two light bars 6 are fixed on 2 bottom surfaces of objective table symmetrically and rotate together with objective table 2, photoelectric door 7 cooperates count time-recorder 8 to measure the time that light bar 6 passes through photoelectric door 7, stay cord 11 is walked around fixed pulley 9 and is connected cone pulley 3 and weight 10, 3 radiuses of cone pulley are the known quantity, different weights 10 or the weight 10 of different quantity produce the moment of variation in size.
Set up anti-skidding structure through the top at objective table 2 for when placing on objective table 2 suddenly around main shaft pivoted test piece 1 originally, test piece 1 can rotate simultaneously with objective table 2, makes test piece 1 move with objective table 2 between the relative slip ground in enough short time, thereby makes the influence of friction moment negligible on main shaft 4, and then verifies the law of conservation of angular momentum.
In one particular embodiment:
a plurality of wheel surfaces with uniformly increasing radiuses are arranged on the cone pulley 3 along the axis direction, the radius of the wheel surface of one end of the cone pulley 3 close to the objective table 2 is the largest, and the radius of the wheel surface is gradually decreased towards the direction far away from the objective table 2. The end of the pull cord 11 may be removably attached to each tread.
A base 5 is arranged below the cone pulley 3, the base 5 is rotatably connected with the cone pulley 3 through a main shaft 4, and the photoelectric door 7 and the fixed pulley 9 are both arranged on the base 5.
In another specific embodiment:
the principle of measuring the moment of inertia by a constant moment rotation method is as follows:
according to the fixed-axis rotation law of the rigid body:
M＝Jβ (1)
the moment of inertia J of the rigid body can be calculated by measuring the total external moment M borne by the rigid body during rotation and the angular acceleration beta of the rigid body under the action of the moment.
Let the moment of inertia of the platform 2, which is empty and rotates at a certain initial angular velocity, be J 1 When the weight 10 is not added, the frictional resistance moment M μ Under the action of (2), the object stage will accelerate at an angular acceleration beta 1 Making uniform deceleration movement, namely:
-M μ ＝J 1 β 1 (2)
a weight 10 with mass m is connected to an objective table 2 through a pull rope 11, the pull rope 11 is wound on a cone pulley 3 with radius R, the weight 10 is allowed to fall, and the system can do uniform accelerated motion under the action of constant external force. If the acceleration of the weight 10 is "a", the tension applied to the rope 11 is "T ═ m (g-a)", where g is the acceleration of gravity, and in general, g is 9.8m/s 2 . If the angular acceleration of the stage 2 is beta at this time 2 Then a ═ R β 2 . The moment applied to the stage 2 by the pull rope 11 is T R ═ m (g-R β) 2 ) R, this time:
m(g-Rβ 2 )R-M μ ＝J 1 β 2 (3)
will (a) to2) And (3) simultaneous elimination of M μ After that, it is possible to obtain:
similarly, if the moment of inertia of the system is J after the object to be measured is added on the object stage 2 2 The angular accelerations of the front and rear of the additional weight 10 are respectively beta 3 And beta 4 Then, there are:
the moment of inertia J of the tested sample can be obtained by the superposition principle of the moment of inertia 3 Comprises the following steps:
J 3 ＝J 2 -J 1 (6)
r, m and beta are measured 1 、β 2 、β 3 、β 4 The moment of inertia of the measured pattern can be calculated by the formulas (4), (5) and (6).
Measurement of β:
in the experiment, a counting timer 8 is adopted to record the shielding times and corresponding moments. Two light-blocking bars 6 fixed on the circumferential edge of the object stage 2 with a pi angle difference shelter the photoelectric gate 7 fixed on the base 5 once per half rotation, namely a counting photoelectric pulse is generated, and the counter counts down the shielding times k and the corresponding time t. Counting and timing are started from the first light blocking (k is 0, t is 0), and the initial angular velocity is ω 0 Then for any two sets of data (k) measured in the uniform variable speed motion m ，t m )、(k n ，t n ) Corresponding angular displacement theta m 、θ n Respectively as follows:
eliminating omega from (7) and (8) 0 The following can be obtained:
the angular acceleration β can be calculated from the expression (9).
The angular acceleration and the moment of inertia of the test piece 1 to be tested can be measured by the experimental device by the method described above.
Before the experiment of the technical scheme, the experimental device is leveled, the height and the direction of the fixed pulley 9 are adjusted, the pulley groove of the fixed pulley 9 is equal to the height of the step pulley 3, the directions of the pulley groove and the step pulley are vertical to each other, and the counting timer 8 is connected with the photoelectric door 7 by a data line.
The objective table 2 is slightly stirred by hand, so that the objective table 2 has an initial rotating speed and performs uniform deceleration movement. After the object stage 2 rotates for 3 circles, the switch of the counting timer 8 is pressed to start recording data, the object stage 2 rotates for at least 3 circles again and stops measuring, the light blocking times and the corresponding moment data on the counting timer 8 are consulted, and the angular acceleration beta in the deceleration process is calculated according to the formula (9) 1 。
Selecting the radius R of the wheel surface of the cone pulley 3 and the mass m of the weight 10, fixedly connecting one end of a pull rope 11 to the wheel surface of the selected cone pulley 3, closely winding the pull rope on the wheel surface in a non-overlapping mode, and connecting the other end of the pull rope 11 to the weight 10 after passing through a fixed pulley 9. The objective table 2 is stabilized by hand, then the objective table 2 is released, the constant torque generated by the gravity of the weight 10 enables the objective table 2 to generate uniform acceleration rotation, and meanwhile, the switch of the counting timer 8 is pressed to start recording data. Recording at least 6 groups of data, stopping measurement, looking up light blocking times and corresponding time data on the counting timer 8, and calculating angular acceleration beta of the acceleration process according to formula (9) 2 . The moment of inertia J of the stage 2 is calculated according to the formula (4) 1 。
The objective table 2 is slightly stirred by hand, so that the objective table 2 has an initial rotating speed and performs uniform deceleration movement under the action of friction torque. After the object stage 2 rotates 3 times, the switch of the counting timer 8 is pressed to start recording data. After the object stage 2 rotates at least 3 times again, the object stage willThe test piece 1 which originally does not rotate around the main shaft is horizontally placed on the objective table 2, and the measurement is stopped after the test piece rotates for at least 3 circles. Looking up the light blocking times and the corresponding time data on the counter timer 8, judging the falling time of the test piece 1 according to whether the time difference between two adjacent times is significant, after eliminating a group of data before and after the falling time (eliminating unstability influence), calculating the angular speed before falling omega pi/delta t and the angular speed after falling omega ' pi/delta t ' by using the time difference between the 2 nd and 3 rd groups of times before and after falling (namely delta t and delta t '). Thus, the angular momentum L of the pivoting of the object stage 2 before the landing can be obtained 1 ＝J 1 X ω, since the angular momentum of the test piece 1 around the axis before the landing is zero, the total angular momentum L of the stage 2 and the test piece 1 around the axis before the landing is L 1 ＝J 1 ×ω。
The total moment of inertia J of the rotation of the stage 2 and the specimen 1 is calculated similarly to the above steps without changing the relative positions of the specimen 1 and the stage 2 2 . The total angular momentum L' J of the pivoting of the object table 2 and the test piece 1 after the lowering can then be obtained 2 ×ω’。
The law of conservation of angular momentum can be verified by the fact that the relative error of L and L '(L-L')/L is negligible and small.
The above-mentioned embodiments only express the specific embodiments of the present invention, and the description thereof is specific and detailed, but not construed as limiting the scope of the present invention. It should be noted that, for those skilled in the art, without departing from the spirit of the present invention, several variations and modifications can be made, which are within the scope of the present invention.
The above-mentioned embodiments only express the specific embodiments of the present invention, and the description thereof is specific and detailed, but not construed as limiting the scope of the present invention. It should be noted that, for those skilled in the art, without departing from the spirit of the present invention, several variations and modifications can be made, which are within the scope of the present invention.
Claims (10)
1. An experimental device for verifying the law of conservation of angular momentum, comprising:
the top of the object stage (2) is provided with an anti-skidding structure, and the object stage (2) can rotate;
the light blocking rod (6) is arranged on the objective table (2);
a photoelectric gate (7) which can be coupled with the light-blocking rod (6);
and the counting timer (8) is electrically connected with the photoelectric gate (7).
2. Experimental device for verifying the law of conservation of angular momentum as claimed in claim 1,
the anti-slip structure is an anti-slip layer or an anti-slip mat (12).
3. Experimental device for verifying the law of conservation of angular momentum as claimed in claim 1,
two sides of the bottom of the objective table (2) are respectively and symmetrically provided with one light blocking rod (6);
the photoelectric door (7) is positioned below the objective table (2).
4. The experimental apparatus for verifying the law of conservation of angular momentum as claimed in claim 1, further comprising:
the cone pulley (3) is arranged at the bottom of the objective table (2);
one end of the pull rope (11) is connected with the cone pulley (3);
the pulling rope (11) can be wound on the cone pulley (3), and the pulling rope (11) is connected with the objective table (2) through the cone pulley (3).
5. Experimental device for verifying the law of conservation of angular momentum as claimed in claim 4, characterized in that said cone pulley (3) is provided with a plurality of wheel surfaces with uniformly increasing radii along the direction of its axis;
the pull rope (11) can be detachably connected with the wheel surface of each cone pulley (3) respectively and wound on the corresponding wheel surface.
6. Experimental device for verifying the law of conservation of angular momentum as claimed in claim 5, wherein said drawing ropes (11) are densely wound on the tread of said step pulley (3) in a non-overlapping manner.
7. The experimental apparatus for verifying the law of conservation of angular momentum as claimed in claim 4, further comprising:
and the power part is connected with one end of the pull rope (11) far away from the cone pulley (3).
8. Experimental device for verifying the law of conservation of angular momentum as claimed in claim 7, characterized in that said power section comprises a plurality of weights (10).
9. The experimental apparatus for verifying the law of conservation of angular momentum as claimed in claim 4, further comprising:
a base (5);
the bottom of the cone pulley (3) is rotatably connected to the base (5), and the photoelectric door (7) is located on the base (5).
10. The experimental apparatus for verifying the law of conservation of angular momentum as claimed in claim 4, further comprising:
a fixed pulley (9);
stay cord (11) are walked around fixed pulley (9), just stay cord (11) are located fixed pulley (9) with one section between cone pulley (3) is the level form, another section of stay cord (11) is vertical form.
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| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202220575038.1U CN217214003U (en) | 2022-03-14 | 2022-03-14 | Experimental device for verifying conservation of angular momentum law |
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| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202220575038.1U CN217214003U (en) | 2022-03-14 | 2022-03-14 | Experimental device for verifying conservation of angular momentum law |
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| CN217214003U true CN217214003U (en) | 2022-08-16 |
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| CN202220575038.1U Active CN217214003U (en) | 2022-03-14 | 2022-03-14 | Experimental device for verifying conservation of angular momentum law |
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