JP5566248B2 - Hanging device and center of gravity position measuring method - Google Patents

Description

  The present invention relates to a suspension device and a center-of-gravity position measuring method.

  There are cases where it is desired to know the position of the center of gravity of an object. For example, a container having a center of gravity deviated from side to side or at a very high position is not preferable because the movement performance of a container vehicle on which the container is mounted is significantly reduced. Therefore, it is very important to know the position of the center of gravity of the container in advance. From such a background, an apparatus for measuring the position of the center of gravity of an object has been proposed in the past (see, for example, Patent Document 1).

JP 2010-85182 A

  However, all of the conventionally proposed center-of-gravity position measurement devices have to perform work only for obtaining data necessary for calculation of the center-of-gravity position, and the work efficiency is not necessarily high. On the other hand, if the data for calculating the center of gravity of the object (container) can be acquired with some work (for example, with the work of unloading the container from the container ship), the efficiency of the work as a whole is very high.

  The present invention has been made in order to solve the above-described problems, and is a suspension device that can acquire necessary data in a state where the object is suspended and can calculate the position of the center of gravity of the object. It is another object of the present invention to provide a center-of-gravity position measurement method capable of acquiring necessary data in a state where the object is suspended and calculating the center-of-gravity position of the object.

  The present invention has been made to solve the above-described problems, and a suspension device according to the present invention supports a suspension unit that is movable in a state in which an object is suspended, and the object. A plurality of suspension wires that connect the suspension portion and the support portion, an operation portion that controls a moving speed of the suspension portion to cause horizontal free vibration in the object, A calculation unit that calculates the center of gravity position of the object, and in the vibration direction of the object, the distance between the fulcrums on the suspension part side of the suspension wire is different from the distance between the fulcrums on the support part side. The calculation unit is configured such that the weight of the object, the vibration period of free vibration generated in the object, the suspension distance between the suspension part and the support part, the suspension part side Distance between fulcrums, distance between fulcrums on the support side, and Based on the moment of inertia around heart, and calculates the barycentric position in the vertical direction of the object.

  In the above-described suspension device, the suspension device further includes a winding device that winds up each of the suspension wires and changes a suspension distance between the suspension portion and the support portion, and the calculation unit includes the calculation unit, The first vibration cycle, which is the vibration cycle of the object when the suspension distance is the first suspension distance, is acquired, and the vibration cycle of the object when the suspension distance is the second suspension distance. The second vibration cycle is acquired, and the calculation unit is configured to determine the weight of the object, the first vibration cycle, the second vibration cycle, the first suspension distance, the second suspension distance, and the suspension portion side. The center-of-gravity position in the vertical direction of the object may be calculated without using the moment of inertia around the center of gravity of the object based on the distance between the fulcrums and the distance between the fulcrums on the support side. .

  In the above-described suspension device, the suspension device further includes a load detection unit that detects each suspension load applied to the suspension wire, and the calculation unit is configured to determine the weight of the object based on each suspension load. And a center-of-gravity position in the horizontal direction of the object may be calculated.

  Further, in the above-described suspension device, the calculation unit may be configured to calculate a vibration period of free vibration of the object based on a variation period of the suspension load.

  Furthermore, the center-of-gravity position measuring method according to the present invention suspends an object from a suspension portion using a plurality of suspension wires, and the distance between the fulcrum on the suspension portion side of the suspension wire facing the suspension wire The suspension wires are arranged so that the distances between the fulcrums on the object side are different, the object is freely vibrated in the facing direction of the facing suspension wires, the weight of the object, the suspension part Suspension distance between the object and the object, vibration period of free vibration of the object, distance between the fulcrum on the suspension part side, distance between the fulcrum on the object side, and inertia around the center of gravity of the object Based on the moment, the position of the center of gravity of the object in the vertical direction is calculated.

  Further, in the above-described center-of-gravity position measurement method, a first vibration period that is a vibration period of the object when the suspension distance is the first suspension distance is acquired, and the suspension distance is the second suspension distance. A second vibration period that is a vibration period of the object at the time of obtaining the object, and a weight of the object, the first suspension distance, the second suspension distance, the first vibration period, and the second vibration period. And calculating the position of the center of gravity of the object in the vertical direction without using the moment of inertia around the center of gravity of the object based on the distance between the fulcrums on the suspension part side and the distance between the fulcrum on the object side. It may be.

  According to the hanging device according to the present invention, necessary data can be acquired in a state where the object is suspended, and the center of gravity position of the object can be calculated. Moreover, according to the center-of-gravity position measuring method according to the present invention, necessary data can be acquired in a state where the object is suspended, and the center-of-gravity position of the object can be calculated.

1 is a schematic perspective view of a suspension device according to a first embodiment of the present invention. It is a schematic perspective view in the support part periphery of the hanging apparatus shown in FIG. It is a schematic front view of the hanging apparatus shown in FIG. It is a schematic front view of the hanging apparatus which concerns on 2nd Embodiment of this invention.

  Hereinafter, embodiments of a hanging device according to the present invention will be described with reference to the drawings. Below, the same code | symbol is attached | subjected to the element which is the same or it corresponds through all the drawings, and the overlapping description is abbreviate | omitted.

(First embodiment)
First, the structure of the hanging device 100 according to the first embodiment of the present invention will be described with reference to FIG. FIG. 1 is a schematic perspective view of a suspension device 100 according to the present embodiment. As shown in FIG. 1, the suspension device 100 according to the present embodiment includes a suspension unit 10, a support unit 20, suspension wires 31 to 34, a winding device 40, a load detection unit 50, and an operation. A unit 60 and a calculation unit 70 are provided. Hereinafter, each of these components will be described in order.

  The hanging part 10 is a part that moves together with the object A while the object A is suspended. In this embodiment, the high place rail 90 is provided above the hanging part 10, and the hanging part 10 is configured to be movable in the left-right direction in FIG. 1 along the high place rail 90. . In the lower left of FIG. 1, the directions of XYZ are indicated by arrows, but the Y direction indicates the horizontal direction (left and right direction on the drawing) in which the hanging part 10 moves, and the X direction is orthogonal to the Y direction. The horizontal direction (the depth direction on the paper surface) is shown, and the Z direction is the vertical direction (the vertical direction on the paper surface). This also applies to FIGS. 3 and 4.

  The support part 20 is a part that supports the object A. In the present embodiment, the support unit 20 supports the object A by being coupled to the upper surface portion of the object A. When the object A is a container, corner metal fittings are provided at the four corners of the upper surface thereof, so that the container can be easily supported by connecting a member on the support portion 20 side corresponding to this corner metal fitting to the corner metal fittings. Can do. In addition, the magnitude | size of the support part 20 may be small or large with respect to the upper surface of the target object A, and is not specifically limited.

  The suspension wires 31 to 34 are members that connect the suspension unit 10 and the support unit 20. In this embodiment, four hanging wires 31 to 34 are used. In the following, the respective suspension wires 31 to 34 are arranged in the order of “first suspension wire 31”, “second suspension wire 32”, “third suspension wire 33” in the counterclockwise direction from the front right side of FIG. This is referred to as “fourth hanging wire 34”. Among these, the 1st hanging wire 31 and the 4th hanging wire 34 have opposed in the advancing direction (Y direction) of the hanging part 10. FIG. The distance between the fulcrums on the suspending portion 10 side of the first suspending wire 31 and the fourth suspending wire 34 is configured to be smaller than the distance between the fulcrums on the supporting portion 20 side (toward the vertically downward direction). Configured to spread). Similarly, the second hanging wire 32 and the third hanging wire 33 are opposed to each other in the traveling direction (Y direction) of the hanging portion 10, and the second hanging wire 32 is parallel to the first hanging wire 31. In addition, the third suspension wire 33 is configured to be parallel to the fourth suspension wire 34.

  The winding device 40 is a device for winding the hanging wires 31 to 34. In the present embodiment, the winding device 40 is attached to the hanging portion 10 and is provided at four locations so as to correspond to the four hanging wires 31 to 34, respectively. The winding device 40 can change the suspension distance between the suspension unit 10 and the support unit 20 by winding the suspension wires 31 to 34. In addition, the winding device 40 may be configured to wind all the hanging wires 31 to 34 at the same time, instead of being provided so as to correspond to each of the hanging wires 31 to 34.

  The load detection unit 50 is a device that detects a suspension load (tension) applied to each suspension wire 31 to 34. In the present embodiment, a load cell is employed as the load detection unit 50. The load detection unit 50 is attached to each of the four suspension wires 31 to 34, generates a detection signal corresponding to the suspension load (tension) applied to each of the suspension wires 31 to 34, and transmits the detection signal to the calculation unit 70. To do. In the calculation unit 70, the suspension load (tension) applied to each suspension wire 31 to 34 is calculated based on the detection signal transmitted from the load detection unit 50. Note that the load detection unit 50 is not directly attached to the suspension wires 31 to 34, but is connected to the connection portion of the suspension unit 10 with the suspension wires 31 to 34 or the suspension wires 31 to 34 of the support unit 20. You may attach to a connection part.

  The operation unit 60 is a part for operating the moving speed of the hanging unit 10 and the winding amount of the winding device 40. The operation unit 60 can accelerate and stop the suspension unit 10 to a predetermined speed. The operation unit 60 can swing (freely vibrate) the object A in the moving direction (Y direction) of the hanging unit 10 by changing the speed of the hanging unit 10. In addition, operation of the suspension part 10 and the winding device 40 by the operation part 60 may be performed manually, and may be performed automatically.

  The calculating unit 70 calculates (calculates) the weight of the object A, the vibration period when the object A is freely vibrated, the center of gravity position of the object A in the horizontal direction, and the center of gravity position of the object A in the vertical direction. Part. Among these, the weight of the object A can be calculated based on the suspension load (tension) applied to the suspension wires 31 to 34. The vibration period of the object A can be calculated based on the fluctuation period of the suspension load (tension). This is because the suspension load applied to each suspension wire 31 to 34 also periodically changes as the object A vibrates. A method for calculating the center of gravity position in the horizontal direction and a method for calculating the center of gravity position in the vertical direction will be described later.

  The above is the structure of the hanging device 100 according to the present embodiment. In the above description, the calculation unit 70 calculates the weight of the object A. However, if the weight of the object A is known, the calculation unit 70 does not need to calculate it. Further, the vibration period of the object A may be calculated by the calculation unit 70 based on signals transmitted from the acceleration sensor and the tilt sensor attached to the support unit 20.

  Subsequently, the center-of-gravity position measurement method according to the present embodiment will be described. First, a method for measuring the position of the center of gravity of the object A in the “horizontal direction” will be described with reference to FIG. FIG. 2 is a schematic perspective view of the suspension device 100 around the support portion 20.

  First, the suspended object A is stopped, and the suspension load (tension) of each suspension wire 31 to 34 in this state is acquired. When carrying out a container from a container ship, the container (object A) on the container ship is lifted to a predetermined height by the suspension device 100, the container is temporarily stopped, and the suspension load applied to each suspension wire 31 to 34 Is obtained (calculated).

Next, the calculation unit 70 calculates the position of the center of gravity of the object A in the horizontal direction based on the acquired suspension load. Specifically, as shown in FIG. 2, the center of the fulcrum in the support portion 20 of each suspension wire 31 to 34 is the center O of the coordinates, and the support portions of the first suspension wire 31 and the fourth suspension wire 34 are supported. The distance between the fulcrums at 20 is w ₁ , the distance between the fulcrums at the support portion 20 of the first suspension wire 31 and the second suspension wire 32 is d ₁ , and the suspension load applied to the first to fourth suspension wires 31 to 34 ( Assuming that (tension) is F _{1 to} F ₄ , the coordinates (x _G , y _G ) of the center of gravity G _h in the horizontal direction of the object A can be obtained by the following first and second expressions. Note that the right side of FIG. 2 is the positive area of the y coordinate, and the near side is the positive area of the x coordinate.

  By the above method, the center-of-gravity position of the object A in the horizontal direction can be measured. Note that the calculation (calculation) of the center-of-gravity position in the horizontal direction is not necessarily performed while the object A is stopped, and may be performed during or after the movement.

  Next, a method for measuring the position of the center of gravity of the object A in the “vertical direction” will be described with reference to FIG. FIG. 3 is a schematic front view of the suspending device 100 (viewed from the X direction) and shows a state when the object A that freely vibrates is at the lowest position. The object A vibrates in the left-right direction (Y direction) in FIG.

First, the object A is freely vibrated, and the vibration cycle at that time is acquired. In the present embodiment, the vibration period is acquired twice by changing the vibration condition (changing the suspension distance h between the suspension unit 10 and the support unit 20). First, the vibration period in the first condition is acquired. Speaking of the above example of carrying out the container, after temporarily stopping the container (object A), the suspending part 10 that suspends the container is accelerated in the horizontal direction (Y direction) and stabilized at a constant speed. Thereby, since the container performs free vibration, the vibration cycle at this time is acquired. The suspension distance between the suspension part 10 and the support part 20 in the first condition is “first suspension distance h ₁ ”, and the vibration period of the object A is “first vibration period T ₁ ”. To do.

Next, the vibration period in the second condition is acquired. Speaking of the above example of carrying out the container, after obtaining the vibration period under the first condition, the suspension distance h between the suspension portion 10 and the support portion 20 is changed, and the suspension portion 10 is further stopped. . As a result, the object A performs free vibration with a vibration period different from that in the first condition. The vibration period at this time is acquired. The suspension distance between the suspension part 10 and the support part 20 in the second condition is “second suspension distance h ₂ ”, and the vibration period of the object A is “second vibration period T ₂ ”. To do.

Next, the center-of-gravity position in the vertical direction of the object A is calculated (calculated). The calculation of the center of gravity position is performed by the calculation unit 70. When the object A as shown in FIG. 3 vibrates in the left-right direction (Y direction), the support portion 20 (on the lower side) of the right hanging wire 31 (32) and the left hanging wire 34 (33) is used. ) distance between fulcrums w ₁ and at the lower portion 10 hanging of (the above) the distance between fulcrums w ₂ and the oscillation period of the different translational pendulum T is a hanging distance between the lower portion 10 hanging support 20 When h, the distance from the support 20 to the center of gravity G of the object A is h _G , the weight of the object A is M, the gravitational acceleration is g, and the moment of inertia around the center of gravity of the object A is I Can be obtained.

Here, in the first condition, the vibration cycle T = T ₁ and the suspension distance h = h ₁ , and when α = α _{1 at} this time, the third equation is expressed as the following fourth equation: be able to.

Similarly, in the second condition, since the vibration period T = T ₂ and the suspension distance h = h ₂ , when α = α _{2 at} this time, the third equation is expressed as the following fifth equation: be able to.

In both the fourth and fifth formulas, the distance h _G from the support portion 20 to the center of gravity G of the object A and the moment of inertia I around the center of gravity of the object A are unknown, but the others are known. Therefore, by solving the simultaneous equations of the fourth and fifth equations, the distance h _G from the support 20 to the center of gravity G of the object A and the moment of inertia I around the center of gravity of the object A can be obtained.

  By the above method, the center-of-gravity position of the object A in the vertical direction can be measured. Note that the calculation (calculation) of the center of gravity position in the vertical direction itself does not have to be performed while the object A is vibrating, and may be performed after the vibration.

  The above is the description of the hanging device 100 and the center-of-gravity position measuring method according to the present embodiment. According to the hanging device 100 according to the present embodiment, it is possible to acquire data necessary for calculating the gravity center position of the object A when the object A is moved. Therefore, for example, when the container is unloaded from the container ship and the container is mounted on the container vehicle, the position of the center of gravity of the container can be calculated.

Note that the method of measuring the position of the center of gravity in the vertical direction described above is based on the distance between the fulcrum of the hanging portion 10 of the first hanging wire 31 and the fourth hanging wire 34 (the second hanging wire 32 and the third hanging wire 33). it can be the distance between fulcrums w ₁ for the first time realized in different at the distance w ₂ and the supporting portion 20. In the case of a translational pendulum that vibrates in the left-right direction, the distance between the fulcrum points above the right and left suspending wires 33, 34 is the same as the distance between the fulcrum points below (each suspending point). When the wires 31 to 34 are arranged in parallel with each other), the object A vibrates at the same vibration period regardless of the height position of the center of gravity G of the object A. When the distance between the fulcrum above the lower wire 31, 32 and the left suspending wire 33, 34 is different from the distance between the lower fulcrum (when each of the suspension wires 31 to 34 is disposed obliquely). This is because the vibration period changes depending on the height position of the center of gravity G of the object A.

In the drawings, the distance between fulcrums _{w 2} in the hook member 10 of the first hanging wire 31 fourth hanging wires 34 (second hanging wire 32 and the third hanging wire 33), the supporting portion 20 Although it is illustrated smaller than the fulcrum distance w _{1 at,} the fulcrum distance w ₂ in the hanging portion 10 may be configured to be larger than the fulcrum distance w ₁ in the support portion 20.

  In the above description, when calculating the center of gravity position in the vertical direction, the suspension distance h between the suspension portion 10 and the support portion 20 is changed to change the vibration period of the object A twice under different vibration conditions. The case of measuring is described. However, when the moment of inertia I around the center of gravity of the object A is known, for example, because the shape of the contents of the object A can be assumed, it is not necessary to solve the simultaneous equations. For example, the center of gravity position in the vertical direction can be calculated using only the fourth equation. That is, in this case, it is sufficient to acquire the vibration cycle of the object A once.

  Further, the suspension device 100 according to the present invention may be provided with a display device around the operation unit 60 in order to show the operator the position of the center of gravity of the object A, and further the center of gravity of the object A in the vertical direction. You may provide the alerting | reporting means to notify an operator of danger, when a position is more than fixed.

(Second Embodiment)
Next, the suspension device 200 according to the second embodiment of the present invention will be described with reference to FIG. FIG. 4 is a schematic front view of the suspension device 200 according to the present embodiment, and corresponds to FIG. 3 of the first embodiment. As shown in FIG. 4, the suspension device 200 according to the present embodiment is a suspension device according to the first embodiment in that the support portion 20 is configured to support the object A on its “upper surface”. 100 and the configuration is different. However, the configuration other than this is basically the same as that of the suspension device 100 according to the first embodiment. In addition, description about each structure of the suspending apparatus 200 is abbreviate | omitted.

Subsequently, the center-of-gravity position measurement method according to the present embodiment will be described. Here, only the method of measuring the center of gravity of the object A in the vertical direction will be described. Note that the method of measuring the position of the center of gravity of the object A in the horizontal direction is the same as in the first embodiment. First, as in the first embodiment, the vibration condition is changed (the suspension distance h between the suspension portion 10 and the support portion 20 is changed), the object A is freely vibrated, and the vibration period Is acquired twice. The suspension distance between the suspension part 10 and the support part 20 in the first condition is “first suspension distance h ₁ ”, and the vibration period of the object A is “first vibration period T ₁ ”. To do. In addition, the suspension distance between the suspension part 10 and the support part 20 under the second condition is “second suspension distance h ₂ ”, and the vibration period of the object A is “second vibration period T ₂ ”. To do.

Next, the center-of-gravity position in the vertical direction of the object A is calculated (calculated). As in the present embodiment, when the object A vibrates in the left-right direction (Y direction) and the object A is located on the upper surface of the support portion 20, the right hanging wire 31 (32) and the left hanging wire 34 ( 33) The vibration period T of the translational pendulum in which the inter-fulcrum distance w ₁ in the support portion 20 and the inter-fulcrum distance w ₂ in the suspension portion 10 are different is the suspension distance between the suspension portion 10 and the support portion 20. When h, the distance from the support portion 20 to the center of gravity G of the object A is h _G , the weight of the object A is M, the gravitational acceleration is g, and the moment of inertia around the center of gravity of the object A is I Can be obtained.

Here, in the first condition, the vibration cycle T = T ₁ and the suspension distance h = h ₁ , so if α = α _{1 at} this time, the sixth equation is expressed as the following seventh equation: be able to.

Similarly, in the second condition, since the vibration period T = T ₂ and the suspension distance h = h ₂ , if α = α _{2 at} this time, the sixth expression is expressed as the following eighth expression: be able to.

In both the seventh and eighth expressions, the distance h _G from the support portion 20 to the center of gravity G of the object A and the moment of inertia I around the center of gravity of the object A are unknown, but other than that are known. Therefore, by solving the simultaneous equations of the seventh and eighth equations, the distance h _G from the support portion 20 to the center of gravity G of the object A and the moment of inertia I around the center of gravity of the object A can be obtained.

  The above is the description of the suspension device 200 and the center-of-gravity position measurement method according to the present embodiment. Even in the case where the object A is supported on the upper surface of the support unit 20 as in the present embodiment, the position of the center of gravity of the object A can be calculated while the object A is suspended. For example, when the object A is a container vehicle, the method of the first embodiment is difficult because the upper surface of the container vehicle needs to be supported by the support portion 20, but according to the method of the present embodiment, the container vehicle is self-propelled. If it can move on the support part 20, the gravity center position of the whole container vehicle can be measured.

  The first embodiment and the second embodiment according to the present invention have been described above with reference to the drawings. However, the specific configuration is not limited to these embodiments, and the scope of the present invention is not deviated. Any change in design is included in the present invention.

For example, in the above embodiment, when acquiring the vibration period of the object A, the suspension distance h between the suspension part 10 and the support part 20 is changed, the vibration period is obtained twice, and the simultaneous equations are used. The case where two equations are generated has been described, but instead of this, two equations for simultaneous equations are obtained by changing the inter-fulcrum distances w ₁ and w ₂ between the suspension wires and acquiring the vibration period twice. You may make it produce | generate.

  According to the suspension device according to the present invention related to the present invention, necessary data can be acquired in a state where the object is suspended, the center of gravity position of the object can be calculated, and the center of gravity according to the present invention is obtained. According to the position calculation method, necessary data can be acquired in a state where the object is suspended, and the center of gravity position of the object can be calculated, which is useful in the technical field of center of gravity position calculation.

DESCRIPTION OF SYMBOLS 10 Suspension part 20 Support part 31-34 Suspension wire 40 Winding device 50 Load detection part 60 Operation part 70 Calculation part 90 Altitude rail 100,200 Suspension apparatus A Object

Claims (6)

A suspension part movable in a state where the object is suspended;
A support part for supporting the object;
A plurality of suspension wires connecting the suspension and the support;
An operation unit for controlling a moving speed of the suspension unit to cause horizontal free vibration in the object;
A calculation unit that calculates the center of gravity of the object,
In the vibration direction of the object, the distance between the fulcrum on the hanging part side of the hanging wire is configured to be different from the distance between the fulcrum on the support part side,
The calculation unit includes a weight of the object, a vibration period of free vibration generated in the object, a suspension distance between the suspension part and the support part, a distance between supporting points on the suspension part side, A suspension device that calculates the position of the center of gravity of the object in the vertical direction based on the distance between supporting points on the support side and the moment of inertia around the center of gravity of the object. A winding device that winds up each of the suspension wires and changes a suspension distance between the suspension portion and the support portion;
The calculation unit obtains a first vibration cycle that is a vibration cycle of the object when the suspension distance is the first suspension distance, and the object when the suspension distance is the second suspension distance. Obtaining a second vibration period which is the vibration period of the object;
The calculation unit includes the weight of the object, the first vibration cycle, the second vibration cycle, the first suspension distance, the second suspension distance, the fulcrum distance on the suspension portion side, and the support The suspension device according to claim 1, wherein the center of gravity position in the vertical direction of the object is calculated based on the distance between fulcrums on the part side without using the moment of inertia around the center of gravity of the object. A load detecting unit for detecting each hanging load applied to the hanging wire;
3. The suspension device according to claim 1, wherein the calculation unit calculates the weight of the object based on the respective suspension loads and calculates the position of the center of gravity in the horizontal direction of the object. .   The suspension device according to claim 3, wherein the calculation unit calculates a vibration cycle of free vibration of the object based on a variation cycle of the suspension load. The object is suspended from the suspension part using a plurality of suspension wires, and the distance between the fulcrums on the suspension part side of the suspension wire facing the object is different from the distance between the fulcrum on the object side. Placing each of the hanging wires,
Freely vibrate the object in the facing direction of the opposing suspension wires;
Weight of the object, suspension distance between the suspension part and the object, vibration period of free vibration of the object, distance between supporting points on the suspension part side, distance between supporting points on the object side And a center-of-gravity position measurement method for calculating a center-of-gravity position in the vertical direction of the object based on the moment of inertia around the center of gravity of the object. A first vibration cycle that is a vibration cycle of the object when the suspension distance is the first suspension distance is acquired, and a vibration cycle of the object when the suspension distance is the second suspension distance. A certain second vibration period is acquired,
The weight of the object, the first suspension distance, the second suspension distance, the first vibration period, the second vibration period, the distance between fulcrums on the suspension part side, and the fulcrum on the object side The center-of-gravity position calculation method according to claim 5, wherein the center-of-gravity position in the vertical direction of the object is calculated based on the distance without using the moment of inertia around the center of gravity of the object.

Images