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Mass moment of inertia of circular cone: Moment of Inertia - Right Circular Cone - x and y axis

In order to determine the mass moment of inertia of a flywheel of radius 1. The solid is made of a homogeneous material that weighs lb.

It should not be confused with the second moment of areawhich is used in beam calculations. Technical report, University of Southampton, The best answers are voted up and rise to the top. Featured on Meta. Plane polygon with vertices P 1P 2P 3 ,

  • Post as a guest Name. Tilted solid cuboid of depth dwidth wand length land mass mrotating about the vertical axis axis y as seen in figure.

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  • Solid sphere ball of radius r and mass m. Useful Geometry.

  • Integrating by parts twice, we can write the indefinite integral in the form:. Consider the influence of work-unit design, span of control and span of accountability.

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Introduction: Moment of Inertia

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  • Mass Moment of Inertia about the x axis I xx. Related 4.

Example The right circular cone is formed by revolving the shaded area around the x axis. Similarly, the moment of inertia of the mass of a body is called as the mass moment of inertia. The integration is extended over the entire volume of the body. You also have the option to opt-out of these cookies. Accept Reject Read More. Revenue growth in segments?

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The moment of inertia of the body w. Related Papers Centroids and Moments of Inertia 2. Non-necessary Non-necessary. On t—m mass moment of inertia of circular cone we get mass moment of inertia of the dA — m2 entire plate about the x — axis. Consider a cylinder of radius R, length L and mass density Suppose we cut a circular disc of infinite thickness dz perpendicular to the z-axis at a distance z from the origin. Case - 1 Description As a result of expansion programme, Pidilite Industries has excess capacity

Add a comment. Solid cuboid of height Dwidth Wand length Land mass mrotating about the longest diagonal. Namespaces Article Talk. Moment of inertia of a solid right circular cone Ask Question. Asked 2 years, 7 months ago.

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Community Ads for Obviously, one principal circular cone is through the centroid, perpendicular to the plane. Moment of inertiadenoted by Imass moment the inertia to which an object resists rotational acceleration about a particular axisand is the rotational analogue to mass which determines an object's resistance to linear acceleration. Think of a hoop, mass M radius Rrolling along a flat plane at speed V. Physics for Scientists and Engineers 2nd ed.

It only takes a minute to sign mass moment of inertia of circular cone. Materials » Polymers » Polybutylene » Film Grades. Also, a point mass m at the end of a rod of length r has this same moment of inertia and the value r is called the radius of gyration. In the above table, n would be the unit Cartesian basis e xe ye z to obtain I xI yI z respectively.

Thin inertia of length L and mass mass momentperpendicular to the axis circular cone indrtia, rotating about one end. Triangle with vertices at the origin and at P and Qwith mass mrotating about an axis perpendicular to the plane and passing through the origin. Panagopoulos and G. Mass Moment of Inertia about the z axis I zz. Solid cuboid of height hwidth wand depth dand mass m.

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Sign up using Email and Password. This just means subtracting from the vertex perpendicular moments of inertia found above a factor M a 2. Moment of Inertia about the centroidal y axis y c I YcYc. R is the radius of the circumscribed circle.

Facebook Twitter Youtube linkedin Pinterest. Assuming that the moment of circulaar couple due to friction remains constant, determine the mass moment Sign In. Students also viewed these Civil Engineering questions Determine the mass moment of inertia I z of the solid formed by revolving the shaded area around the z axis. We can easily derive its equation using the two-point form :. Engineering mechanics dynamics By lol eerd.

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Case - xone Description As a result of expansion mass moment of inertia of circular cone, Pidilite Industries has excess capacity Consider a cone of base radius R, height H and mass densityoriented w. However, in some special cases, the problem can be solved using single integrals. A time constant of 3. We can easily derive its equation using the two-point form :.

Thin rod of length L and mass mperpendicular to the axis of rotation, rotating about its center. Community Ads for Post as a guest Name. Radius of Gyration about the centroidal z axis z c k ZcZc. Browse all ». Mathematics Stack Exchange works best with JavaScript enabled.

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What am I doing wrong? Radius of Gyration about the x axis k xx. Centroid from xy -plane C z.

We also use third-party cookies that help us analyze and understand how you use this circupar. Example 5. Download pdf. Accept Reject Read More. The moment of inertia also called the second moment is a physical quantity which measures the rotational inertia of an object. The Finishing Department reports the following data for the month:Equivalent Units of Engineeringmechanicsdynamics7thedition j By Alexandre Dessouki.

The total kinetic energy is. Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. ISBN Centroid from zx -plane C y. Common Beams.

Introduction: Moment of Inertia

Centroid from zx -plane C y. In general, it may not be straightforward to symbolically express the moment of inertia of shapes with more complicated mass distributions and lacking symmetry. Beam Bending.

The integration is extended over the entire volume of the body. This website uses cookies to improve your experience. Non-necessary Non-necessary. Calculate the moment of inertia of the rod. Accept Reject Read More. Case - 1 Description As a result of expansion programme, Pidilite Industries has excess capacity

Email Required, but never shown. Common Areas. Sign up to join this community. It should not be confused with the second moment of areawhich is used in beam calculations. In general, the moment of inertia is a tensorsee below. Sign up using Facebook.

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Mass moment of inertia is used to study of dynamics of rigid body as it gives a measure of resistance to angular motion about an axis. We'll assume you're ok with this, but you can opt-out if you wish. On t—m integration we get mass moment of inertia of the dA — m2 entire plate about the x — axis. You also have the option to opt-out of these cookies. Example 6.

In general, it may not be straightforward to symbolically express the moment of inertia of shapes with more complicated mass inertja and lacking symmetry. Moment of Inertia about the centroidal x axis x c I XcXc. Create a free Team What is Teams? Active 2 years, 7 months ago. Moment of Inertia about the centroidal z axis z c I ZcZc. Mass Moment of Inertia about the x axis I xx.

Purchaserelated transactions Milan Co a womens clothing store purchased circula merchandise from The leads are said to be capacitively coupled. We also use third-party cookies that help us analyze and understand how you use this website. In general case, finding the moment of inertia requires double integration or triple integration. Acquisitions analysis frequently focuses on the total value of the firms involved. Necessary Necessary.

New VP of Community, plus two more community managers. Views Read Edit View history. Stack Overflow for Teams — Collaborate and share knowledge with a private group. Here we have four obvious principal axes: only possible if we have spherical degeneracy, meaning all three principal axes have the same moment of inertia.

Examples of Moments of Inertia

The Mathematical Gazette. Accept all cookies Customize settings. In general, the moment of inertia is a tensorsee below.

This ibertia also correct for a cylinder think of it as a stack of discs about its axis. To obtain the scalar moments of inertia I above, the tensor moment of inertia I is projected along some axis defined by a unit vector n according to the formula:. Regular icosahedron of side s and mass m. Common Areas. Sign up or log in Sign up using Google.

Consider a cylinder of radius Ot, length L and mass density Suppose we cut a circular disc of infinite thickness dz perpendicular to the z-axis at a distance z from the origin. In order to determine the mass moment of inertia of a flywheel of radius 1. Determine the mass moment of inertia Iz of the solid formed by revolving the shaded area around the axis. We can easily derive its equation using the two-point form :.

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Please can you help! Here we have four obvious principal axes: only possible if we have spherical degeneracy, meaning all three principal axes have the same moment of inertia. What about a symmetrical three dimensional molecule? ISBN Active 2 years, 7 months ago.

Km Km 5 5 silver badges 15 15 bronze badges. Russell Johnston, Jr Radius of Gyration about the centroidal z axis z c k ZcZc. New VP of Community, plus two more community managers. Here we have four obvious principal axes: only possible if we have spherical degeneracy, meaning all three principal axes have the same moment of inertia. Solid ellipsoid of semi-axes abc and mass m.

Radius of Gyration about the centroidal x axis x c k XcXc. Featured on Meta. Solid cylinder of radius rheight h and mass m. Sphere shell of radius r 2 and mass mwith centered spherical cavity of radius r 1.

Analyzing Rolling Motion

Enter the email address you signed up with and we'll email you a reset link. A short summary of this paper. Revenue growth in segments? We also use third-party cookies that help us analyze and understand how you use this website. Non-necessary Non-necessary.

Solid sphere ball of radius r and mass m. Mathematics Stack Exchange works best with JavaScript enabled. This just means subtracting from the vertex perpendicular moments of inertia found above a factor M a 2. Ellipsoid solid of semiaxes aband c with mass m.

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Download pdf. Sign In. The leads are said to be capacitively coupled. But opting out of some of these cookies may affect your browsing experience. Determine the mass moment of inertia Iz of the cone. Listed next are common performance measures appearing on balanced scorecards.

Typically this occurs when the mass density is constant, but in some cases the density can vary throughout the object as well. In general, the moment of inertia is a tensorsee below. Mathematical Association. Thin rectangular plate of height hwidth w and mass m Axis of rotation at the center. Thin cylindrical shell with open ends, of radius r and mass m. New VP of Community, plus two more community managers. Centroid from xy -plane C z.

  • Thin circular loop of radius r and mass m. Mass Moment of Inertia about the z axis I zz.

  • Assuming that the moment of the couple due to friction remains constant, determine the mass moment

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  • The moment of inertia also called the second moment is a physical quantity which measures the rotational inertia of an object.

  • First we determine the moment of inertia of the rod about the axis passing through the center of gravity. Determine the moment of inertia lx and express the result in terms of the total mass m of the cone.

Assuming that the moment of the couple due to friction remains constant, determine the mass moment A time constant of 3. Q2: Justify Indicate whether the Materials handling cost per unit?

Geometry Home. When calculating moments of inertia, mass is mass moment of inertia of circular cone to remember that it is an additive function and exploit the parallel axis and perpendicular axis theorems. Right circular cone with radius rheight h and mass mabout the apex. Radius of Gyration about the x axis k xx. Centroid from zx -plane C y. The moment of inertial about either of these axes will be one-half that about the perpendicular-to-the-plane axis.

Right Circular Cone Moment of Inertia Calculation

Solid cuboid of height hwidth wand depth dand mass m. Moment of inertiammass by Imeasures the extent to which an object resists rotational acceleration about a particular axisand is the rotational analogue to mass which determines an object's resistance to linear acceleration. I have a solid cone base radius r, height h, mass M and I need to find the moment of inertia about a diameter of the base as axis. Mathematics Stack Exchange works best with JavaScript enabled. Radius of Gyration about the centroidal y axis y c k YcYc.

  • Centroid from yz -plane C x.

  • In order to determine the mass moment of inertia of a flywheel of radius 1. A short summary of this paper.

  • Mathematics Stack Exchange works best with JavaScript enabled.

  • Sign up to join this community. When calculating moments of inertia, it is useful to remember that it is an additive function and exploit the parallel axis and perpendicular axis theorems.

Training hoursz? Related Papers Centroids and Moments of Inertia 2. However, in some special cases, the problem can be solved using single integrals. Mass moment of inertia is used to study of dynamics of rigid body as it gives a measure of resistance to angular motion about an axis. Click here to sign up.

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Employee turnover rate? Market share? Consider a cone of base radius R, height H and mass densitymass moment of inertia of circular cone w. It is mandatory to procure user consent prior to running these cookies on your website. Consider a cylinder of radius R, length L and mass density Suppose we cut a circular disc of infinite thickness dz perpendicular to the z-axis at a distance z from the origin. Related Papers Centroids and Moments of Inertia 2.

Regular octahedron of side s and mass m. Solid cylinder of ciruclar rheight h and mass m. This expression assumes that the shell thickness is negligible. Connect and share knowledge within a single location that is structured and easy to search. Views Read Edit View history. Also, a point mass m at the end of a rod of length r has this same moment of inertia and the value r is called the radius of gyration.

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This is also correct for a cylinder think of circulzr as a stack of discs about its axis. Moment of inertiadenoted by Imeasures the extent to which an object resists rotational acceleration about a particular axisand is the rotational analogue to mass which determines an object's resistance to linear acceleration. Centroid from xy -plane C z. New VP of Community, plus two more community managers.

Km Km 5 5 silver badges 15 15 bronze badges. Sign up using Email and Password. Solid cylinder of radius rheight h and mass m. Useful Geometry. Download as PDF Printable version. Right circular hollow cone with radius rheight h and mass m.

The center of mass is distance a from the vertex, where. Mathematical Association. Plane polygon with vertices P 1P 2P 3Sign up or log in Sign up using Google.

In the above table, n would be the unit Cartesian basis e xe ye z to obtain I xI yI z respectively. Right circular cone with radius rheight h and mass mabout the apex. Technical report, University of Southampton, Sign up using Facebook.

  • Following are scalar moments of inertia.

  • Example 9.

  • From Wikipedia, the free encyclopedia. It should not be confused with the second moment of areawhich is used in beam calculations.

  • Murali Krishna.

The Finishing Department reports the following data for the month:Equivalent Units of Example 9. Example 5. These cookies do not store any personal information. Accept Reject Read More.

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First we determine the moment of inertia of the rod about the axis passing through the center of gravity. Non-necessary Non-necessary. Product-development cycle time? These cookies do not store any personal information. In each

The cone rolls without slipping on the horizontal X Y plane. Views Read Edit View history. Panagopoulos and G. I've put most of the working below. The best answers are voted up and rise to the top. Sign up to join this community.

Centroid from xy -plane C z. Serway Point mass M at a distance r from the axis of rotation. Question feed. Moment of Inertia about the centroidal z axis z c I ZcZc. Cambridge University Press.

Applications of Integrals

Murali Krishna. Listed next are common performance measures appearing on balanced scorecards. Example 3. Remember me on this computer. Draw a normal curve and identify the approximate location of the following scores.

Wolfram Research. Learn more. Sign up to join this community. This expression assumes that the shell thickness is negligible. Download as PDF Printable version.

Units » Length » Pole rod, Perch. Wikipedia list article. Mathematics Stack Exchange works best with JavaScript enabled. Also, a point mass m at the end of a rod of length r has this same moment of inertia and the value r is called the radius of gyration. Help Learn to edit Community portal Recent changes Upload file. Sign up or log in Sign up using Google. Community Ads for

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Enter the email address you signed up with and we'll email you a reset link. Determine momebt moment of inertia lx and express the result in terms of the total mass m of the cone. The specific weight of the material is?. Engineering Civil Engineering Determine the mass moment of inertia Iz of the cone.

Thin rod of length L and mass mperpendicular to the axis of rotation, rotating about one end. The Mathematical Gazette. Solid cylinder of radius rheight h and mass m. New VP of Community, plus two more community managers.

  • Thin circular loop of radius r and mass m.

  • The leads are said to be capacitively coupled. Assuming the plate to be perpendicular to the z — axis.

  • Regular dodecahedron of side s and mass m. JSTOR

The mass moment of inertia mwss often also known as the rotational inertiaand sometimes as the angular mass. Retrieved on Plane regular polygon with n -vertices and mass m uniformly distributed on its interior, rotating about an axis perpendicular to the plane and passing through its barycenter. Think of a hoop, mass M radius Rrolling along a flat plane at speed V. Radius of Gyration about the centroidal z axis z c k ZcZc. Physics for Scientists and Engineers 2nd ed.

Active 2 years, 7 months ago. Common Areas. Right circular hollow cone with radius rheight h and mass m. When calculating moments of inertia, it is useful to remember that it is an additive function and exploit the parallel axis and perpendicular axis theorems. Featured on Meta. Ellipsoid solid of semiaxes aband c with mass m. Materials » Polymers » Polybutylene » Film Grades.

Determine the mass moment of inertia Iz of the coe formed by revolving the shaded area around the axis. A short summary of this paper. Determine the radius of gyration ky. These cookies will be stored in your browser only with your consent. We'll assume you're ok with this, but you can opt-out if you wish.

  • Solid ellipsoid of semi-axes abc and mass m.

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  • Download as PDF Printable version. Please can you help!

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Download as PDF Printable version. Active 4 years, 8 months ago. It only takes a minute to sign up. A disc about a line through its center in its plane must be 1 4 M a 2 from the perpendicular axis theorem. Thin cylindrical shell with open ends, of radius r and mass m.

Mathematics Stack Exchange works best with JavaScript enabled. Cambridge University Press. In general, it may not be straightforward to symbolically express the moment of inertia of shapes with more complicated mass distributions and lacking symmetry. The moment of inertia of the hydrogen molecule was historically important.

Email Required, but never shown. Moment of inertia of potentially tilted cuboids. Toggle Menu. This puts the tip at the axis. Radius of Gyration about the y axis k yy. Active 4 years, 8 months ago.

JSTOR The best answers are voted up and rise to the top. Email Required, but never shown.

In general case, finding the moment of inertia requires double integration or triple integration. Necessary cookies are absolutely essential for the website to function properly. The cone has a constant density?. Enter the email address you signed up with and we'll email you a reset link. Market share?

Download Free PDF. Indicate whether the Example 7. The integration is extended over the entire volume of the body.

Market share? Consider the inertiq of work-unit design, span of control and span of accountability. Engineeringmechanicsdynamics7thedition j By Alexandre Dessouki. Suppose now that the rod is rotated about the axis passing through one of the ends. Integrating by parts twice, we can write the indefinite integral in the form:. Calculate the moment of inertia of the rod. Determine the mass moment of inertia Iz of the cone.

Example 4. The right circular cone is formed by revolving mass moment of inertia of circular cone shaded area around the x axis. Consider a cylinder of radius R, length L and mass density Suppose we cut a circular disc of infinite thickness dz perpendicular to the z-axis at a distance z from the origin. An acquisition, however, will usually affect relative

Thus, we see that the moment of inertia of the infinite lamina has the finite value equal to. Knertia the mass moment of inertia Iz of the solid formed by revolving the shaded area around the axis. Suppose now that the rod is rotated about the axis passing through one of the ends. Training hoursz? As the function in the integrand is even, we can rewrite the integral in the form. Sign In.

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Learn more. Here we have four obvious principal axes: only possible if we have spherical degeneracy, conee mass moment of inertia of circular cone three principal axes have the same moment of inertia. Sign up using Facebook. In general, it may not be straightforward to symbolically express the moment of inertia of shapes with more complicated mass distributions and lacking symmetry. All of the above results assume that the body has constant density. A disc about a line through its center in its plane must be 1 4 M a 2 from the perpendicular axis theorem. Active 2 years, 7 months ago.

Materials handling cost per unit? An acquisition, however, will usually affect relative This website uses cookies to improve your experience. The specific weight of the material is?. But opting out of some of these cookies may affect your browsing experience. A time constant of 3. Need more help!

  • Regular tetrahedron of side s and mass m.

  • Mass moment of inertia is used to study of dynamics of rigid body as it gives a measure of resistance to angular motion about an axis. Students also viewed these Civil Engineering questions Determine the mass moment of inertia I z of the solid formed by revolving the shaded area around the z axis.

  • An ellipsoid of revolution and a sphere of the same mass and radius clearly have the same motion of inertial about their common axis shown. Mathematics Stack Exchange works best with JavaScript enabled.

  • Necessary Necessary. However, in some special cases, the problem can be solved using single integrals.

Radius of Gyration about the centroidal y axis y c k YcYc. New VP of Community, plus two more community managers. Mathematics Stack Exchange works best with JavaScript enabled. Sign up using Facebook. Tilted solid cuboid of depth dwidth wand length land mass mrotating about the vertical axis axis y as seen in figure. Retrieved Active 4 years, 8 months ago.

To obtain the scalar moments of inertia I above, the tensor moment of inertia I is projected along some axis defined by a unit vector n according to the formula:. Cambridge University Press. The best answers are voted up and rise to the top. Common Areas.

Post as a guest Name. I have a solid cone base radius r, height h, mass M and I need to find the moment of inertia about a diameter of the base as axis. JSTOR Plane polygon with vertices P 1P 2P 3 ,

Regular tetrahedron of side s cjrcular mass m. Active 2 years, 7 months ago. Physics for Scientists and Engineers 2nd ed. NOTE: is the mass of the entire body. Radius of Gyration about the centroidal y axis y c k YcYc. Solid cylinder of radius rheight h and mass m.

Solve Prob. Example maws. The cone has a constant density?. View Answer. Thus, we see that the moment of inertia of the infinite lamina has the finite value equal to. To what extent did cost-plus pricing contribute to the decline in total sales revenues? This category only includes cookies that ensures basic functionalities and security features of the website.

Indicate whether you circcular the following claims regarding takeovers are true or false. Get help from Civil Engineering Tutors. Determine the mass moment of inertia Iz of the solid formed by revolving the shaded area around the axis. Determine the mass moment of inertia Iz of the cone. On t—m integration we get mass moment of inertia of the dA — m2 entire plate about the x — axis.

Consider a cone of base radius R, height H and mass densityoriented w. Students also viewed these Civil Conr questions Determine the mass moment of inertia I z of the solid formed by revolving the shaded area around the z axis. Materials handling cost per unit? Case - 1 Description As a result of expansion programme, Pidilite Industries has excess capacity Determine the radius of gyration ky. Best for online homework assistance. The solid is made of a homogeneous material that weighs lb.

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Right circular hollow cone with radius rheight h and mass m. Here we have four obvious principal axes: only possible if we have spherical degeneracy, meaning all three principal axes have the same moment of inertia. Thin cylindrical shell with open ends, of radius r and mass m. Moment of Inertia about the centroidal y axis y c I YcYc. Asked 6 years, 6 months ago.

Murali Krishna, M. How might City Steel determine the price at which it sells steel? The density of the material is? These cookies will be stored in your browser only with your consent. Revenue growth in segments?

Sign up using Email and Password. Wikipedia list article. Radius of Gyration about the centroidal x axis x c k XcXc.

Download as PDF Printable version. So I was trying to do this using triple integrals I know there are simpler ways when I encountered something I can't really justify. Moment of inertia of a solid right circular cone Ask Question. Obviously, one principal axis is through the centroid, perpendicular to the plane. Sign up using Facebook.

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Electrocardiographs are often niertia as shown in Fig. Download Free PDF. Engineeringmechanicsdynamics7thedition j By Alexandre Dessouki. Indicate whether the Close Privacy Overview This website uses cookies to improve your experience while you navigate through the website. Download pdf. Consider a cylinder of radius R, length L and mass density Suppose we cut a circular disc of infinite thickness dz perpendicular to the z-axis at a distance z from the origin.

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The cone rolls without slipping on the horizontal X Y plane. Beam Bending. Sign up using Facebook. Obviously, one principal axis is through the centroid, perpendicular to the plane.

Sign In. Example 4. These cookies will be stored in your browser only with your consent. Determine the mass moment of inertia Iz of the cone. Revenue growth in segments? Example 3. Remember me on this computer.

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