What is Center of gravity: Definition and 172 Discussions

In physics, the center of mass of a distribution of mass in space (sometimes referred to as the balance point) is the unique point where the weighted relative position of the distributed mass sums to zero. This is the point to which a force may be applied to cause a linear acceleration without an angular acceleration. Calculations in mechanics are often simplified when formulated with respect to the center of mass. It is a hypothetical point where the entire mass of an object may be assumed to be concentrated to visualise its motion. In other words, the center of mass is the particle equivalent of a given object for application of Newton's laws of motion.
In the case of a single rigid body, the center of mass is fixed in relation to the body, and if the body has uniform density, it will be located at the centroid. The center of mass may be located outside the physical body, as is sometimes the case for hollow or open-shaped objects, such as a horseshoe. In the case of a distribution of separate bodies, such as the planets of the Solar System, the center of mass may not correspond to the position of any individual member of the system.
The center of mass is a useful reference point for calculations in mechanics that involve masses distributed in space, such as the linear and angular momentum of planetary bodies and rigid body dynamics. In orbital mechanics, the equations of motion of planets are formulated as point masses located at the centers of mass. The center of mass frame is an inertial frame in which the center of mass of a system is at rest with respect to the origin of the coordinate system.

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  1. P

    Center of mass vs. center of gravity

    Are there any realistic scenarios for which center of mass is not almost exactly equivalent to the c.o.g., i.e. they must be treated separately?
  2. P

    Center of gravity of an orbitting body not at center of gravity

    It just occurred to me that in the right gravitational field, say, in a low orbit 100 km from the core of a neutron star with a mass equal to that of the sun, an orbiting object's center of gravity is somewhat noticeably displaced from its center of mass. Specifically, 1 meter closer to the...
  3. G

    Center of gravity & moment of inertia

    Dear forum, while standing, spreading your legs helps your stability because you have a wider base. but doesn't spreading your legs lowers your center of gravity, thus shortening the distance (r) from your center of gravity to the ground, and therefore lowering your moment of inertia = making...
  4. adjacent

    Why does a seesaw still lean even when the forces are equal on both sides?

    On the diagram in the thumbnail,You could see A,B,C,D I read from somewhere that forces acting on the two sides should be equal to be in equilibrium But a person moving closer does not change the forces i.e the forces on the two sides is still equal and the center of gravity still lies on the...
  5. D

    Time for Object to Fall Based on Center of Gravity

    Homework Statement This has a fairly long problem statement, so I'll condense it. There are two gates with 81 vertical pickets and two horizontal support bars. These are holo rectangular tubes. The pickets are 2" x 2" x 3/16" box beams and support bars are 4"x6"x3/16" Box Beams. One...
  6. C

    A pickle in finding vehicle center of gravity.

    So I'm trying to find vehicle center of gravity, but i only have this information: full loaded vehicle weight(3200kg or 31392 N) empty vehicle weight(2000kg or 19620 N) maximum rear axle capacity(1500kg or 14715 N) maximum front axle capacity(1800kg or 17658 N) Is this possible? I have a book...
  7. J

    Center of Gravity and Centrifugal Force

    Hi, I have this problem that I'm trying to solve and it has been a few years since I've taken Physics. I want to know how you would approach and solve this problem, and what equations you would use. Hopefully somebody here can help me out. The Problem: A vehicle is on a road that is V inches...
  8. R

    Calculating Wheel Forces on a Car's Center of Gravity

    Homework Statement An automobile with a mass of 1321 kg has 3.40 m between the front and rear axles. Its center of gravity is located 1.78 m behind the front axle. (a) With the automobile on level ground, determine the magnitude of the force from the ground on each front wheel (assuming equal...
  9. M

    Center of gravity and Center of mass different?

    Center of gravity and Center of mass different?? I was developing a test for my students and always look for a difficult question as the only bonus question. I came across the question in the book, "When are center of gravity and center of mass different?". I thought about it before looking at...
  10. L

    Center of Gravity/ Seesaw problem?

    Homework Statement A large wooden beam weighs 820 N and is 3.2 m long. the beam's CG is 1.4 m from one end. two workers carry it away. If they lift the beam at its ends, what part of the weight does each worker lift? Homework Equations Tcw=Tccw F*l=F*l The Attempt at a Solution I...
  11. J

    Calculating Center of Gravity: Bethany, Serendipity & Cardinal Glick

    Homework Statement If Bethany and Serendipity each exert a force of 350 N on each arm of a wheelbarrow with 1.25 m arms and carry Cardinal Glick in the bucket, who has a weight of 1,050 N, where is the center of gravity of the bucket and the Cardinal with respect to the wheel? Pointers would...
  12. R

    Can AutoCAD accurately determine the center of gravity for my vehicle design?

    HELLO Can someone help me locate the center of gravity for my vehicle design? all the parts, dimensions and mass of the parts of the design are known. Is it possible to locate for the COG of it? Thanks!
  13. B

    Exploring Beam Deflection: Area Moment, Moment of Inertia & Center of Gravity

    Homework Statement Hey In my assignment I am writing about beamdeflection, but there's some things i really can find out how to do. I need to explain area moment, moment of inertia and the center of gravity, i need to explain this with the help of integration. Under her I've inertet...
  14. C

    Center of Gravity in a Horizontal Cylinder with Water

    Homework Statement I need to find the center of gravity of a horizontal cylinder that has water in it, the level of water changes so I need to determine a relation between the diameter occupied by the water and the masses, those are my guesses. I solved the problem where i have the standing...
  15. L

    Self-balancing center of gravity shifter system

    I should say that while I've taken some physics courses, I should probably be considered a layman or hack as I haven't done any real world engineering. I'd love to hear some more expert feedback on this topic. I'm sure that there are many approaches to this concept. For this project, my goal...
  16. S

    How to Locate the Center of Gravity

    Hi, I have some questions regarding on the locating of the center of gravity. I have read some txtbk regarding on finding the COG for structure/element that is homogeneous. Therefore, the COG will conincide with the centroid of the the volume. Am i right to say that homogeneous...
  17. H

    Center of Gravity of a Carpenter's Square

    Homework Statement A carpenter's square has the shape of an L, where d1 = 19.0 cm, d2 = 2.00 cm, d3 = 2.00 cm, d4 = 9.0 cm. Locate its center of gravity. (Take (x, y) = (0, 0) at the intersection of d1 and d4.) Picture ---> http://www.webassign.net/pse/p12-07alt.gif Answer = (____...
  18. L

    Finding the tipping point (height at which metacentre = center of gravity?)

    Well, I spent literally 45 minutes typing an in-depth post explaining the problem, the variables, and my (probably incorrect) approach only to be logged out and having the post completely lost after pressing the preview button. Sigh... apologies if it's not as thorough now, but I've run out of...
  19. C

    Center of gravity (x and y coordinates) of mechinist's square

    Homework Statement The machinist's square shown in the figure consists of a thin, rectangular blade connected to a rectangular handle. Determine the x and y coordinates of the center of gravity. Let the lower corner be x=0, y=0. Homework Equations x_cg = (m_1 * x_1)+(m_2 *...
  20. J

    Center of gravity in wrong place?

    Textbooks all say that the center of gravity of an object is the point at which all it's gravitaional effects appear to be concentrated. But that seems to depend on who's checking. (see atachment) Imagine a small mass M some distance from the Earth. That mass is attracted simultaneously...
  21. N

    What is center of gravity espcially for triangles

    What is ceter of gravity concept and how to calculate it for a triangle
  22. U

    Torque- rigid objects in equalibrium/ center of gravity.

    Homework Statement A uniform door(.81m wide and 2.1m high) weighs 140N and is hung on two hinges that fasten the long left side of the door to a vertical wall. The hinges are 2.1m apart. Assume that the lower hinge bears all the weight of the door. Find the magnitude and direction of the...
  23. S

    Biomechanics - Center of Gravity and Projectile Motion - PLEASE help

    1. My professor explained this concept before, but I didn't quite understand. I need help with understanding how if two players jump for the ball with the exact same mass and body segment dimensions, taking off with the same vertical and horizontal velocity of the CoG, one can have an advantage...
  24. T

    How to calculate center of gravity? emergency

    Sorry if this is posted in the wrong section I'm trying to find out what would be a good pick point on a steel point instead of just winging it. There are two sections to the steel pole, both combined together to create a total of 78 feet. The first section is 40' and weighs 3,438.004...
  25. M

    How Does Adding Ballast Affect the Center of Gravity in a Barge?

    Homework Statement <a href="http://www.flickr.com/photos/56362284@N04/6149231787/" title="untitled by redmond0991, on Flickr"><img src="http://farm7.static.flickr.com/6065/6149231787_e6230d69ab.jpg" width="407" height="229" alt="untitled"></a>...
  26. N

    Center of gravity and Newton's 3 Law of Motion.

    I have a project to do and I have to make a demonstration about a physics phenomenon. I'n planning on doing a demonstration that explains one or all of Newton's Laws of Motion. I've chosen to do it on the center of gravity, but I want to know if it's related to Newton's 3 Laws of Motion or is it...
  27. B

    Strange: Earth's center of gravity

    Hi there, so I'm a bit confused...I'm 14 years old and I'm living in Croatia.I heard for Hallow Earth theory one year ago so I wanted to research it, but I had no material i needed until today...data(material9 i needed is what is radius of Earth on poles and Equator and what g is there...
  28. Femme_physics

    Dividing over zero while calculating center of gravity - Getting error

    Homework Statement Calculate the center of gravity of this object: http://img638.imageshack.us/img638/8412/inddddd.jpg The Attempt at a Solution The bottom line turns out zero, so I get something over zero therefor error! http://img101.imageshack.us/img101/6995/theretherere.jpg
  29. Femme_physics

    Center of gravity - conflicting result

    From some reason Yc's result is different than mine. But, the solution manual and me are using the same X axis to calculate Yc (we're using a different Y axis to calculate Xc, though). Can someone explain to me what's wrong here?The question: Calculate the center of mass of the material line...
  30. C

    How Do You Calculate the Center of Mass for a Non-Uniform Object?

    Could anyone help me figure out a formula to calculate a Center of mass for a non uniform object. In my case it would be a "shell" that would go over a body of a solar car. If anyone could help me that would be great.
  31. P

    Center of Gravity questions - Center of Area

    Homework Statement Find the problem of the centroid of each of the shapes http://img29.imageshack.us/img29/7563/64279412.jpg this makeshift diagram is not as accurate as it should be, but it is a plain T shape that is perfectly symmetrical. Homework Equations...
  32. J

    Calculate center of gravity of eco marathon aka supermileage

    Hi, hope someone can help. I need to find the centre of gravity of a supermileage. Here is the dimensions: ~The maximum height must be less than 100 cm. ~ The maximum height measured at the top of the Driver's compartment must be less than 1.25 times the maximum track width between the...
  33. S

    Moon Center of Mass/ Center of Gravity

    Hi, I was wondering about an issue that we just started in my physics class: we learned that center of mass (CM) and center of gravity (CG) coincide in an object as long as the force of gravity is uniform over that object. So, for something near the Earth's surface we can say that CM and CG...
  34. P

    Question regarding acceleration, torque and center of gravity

    These questions apply to the act of pitching a professional horseshoe. I will use a 3 foot rod held horizontally, as an example. Q1. I assume the center of gravity would be 18" from each end. I would grip the rod at the pivot point. Is it true that there is no torque since I'm gripping the...
  35. P

    Uniform plank problem: Center of gravity, equilibrium, and torque

    Homework Statement A uniform plank of length 4.7 m and weight 207 N rests horizontally on two supports, with 1.1 m of the plank hanging over the right support (see the drawing). To what distance x can a person who weighs 454 N walk on the overhanging part of the plank before it just begins to...
  36. B

    Center of Gravity and a Balanced TV Stand

    I am building a stand for my LCD/LED TV and Mount. See several pics below: Calculation Sheet, Mount Diagrams, and Side View of the TV. The Mount will be hanging on 2 poles, and the TV hangs on the front of the Mount. Am I computing the Center of Gravity correctly? in order to determine where to...
  37. P

    How to find the normal force given the center of gravity and the radius

    Homework Statement a person is doing pushups and its weight is 584 N, center of gravity is at waist and from waist to hands=.410m and from waist to feet=.840m. find the normal force on each hand and each foot Homework Equations The Attempt at a Solution do u have to find the...
  38. M

    Relation between centre of mass and center of gravity?

    Homework Statement What is the Relation between center of mass and center of gravity, please compare with simple example. Bco'z i am very confused about it Homework Equations The Attempt at a Solution
  39. H

    Center of Gravity: Locate on Uniform Board 20cmx10cm

    Center of gravity? A uniform board 20.0cm x 10.0 cm has a mass of 200g. Masses of 50.0 and 80.0 grams are attached at two corners at the ends of one of the longer sides. Locate the center of gravity. i have no idea how to solve this help me pls...
  40. V

    Simplex splitting using center of gravity

    hello to all INTRODUCTION: i have created application that splits triangles (2d simplex) and tetrahedrons (3d simplex) to 1 triangle -> 3 quadrilaterals 1 tetrahedron -> 4 bricks (8 nodal elements) my application uses element center of gravity in both cases. and than splits...
  41. S

    What Happens When You Reach the Center of the Earth?

    Suspend all disbelief and imagine digging to the center of the Earth, there you dig out a small spherical chamber, you sit in the middle, do you float or are you depatched violently to the wall around you instantaneously.
  42. M

    Finding center of gravity with a cut out

    Homework Statement Find the x- and y-coordinates of the center of gravity of a 4.00 ft by 8.00 ft uniform sheet of plywood with the upper right quadrant removed as shown in the figure below. The dimensions of the cutout are a = 3.50 ft and b = 2.10 ft. The Attempt at a Solution I made...
  43. T

    Engineering Statics Center of Gravity Problem

    Homework Statement For the machine element shown, locate the x coordinate of the center of gravity. The picture of 2 different problems are attached Homework Equations V = 1/3*a*b*h The Attempt at a Solution I can figure out the coordinates fine for everything except the triangles...
  44. T

    How Does a Skateboarder's Movement Affect Work Done by Forces in a Half-Pipe?

    A skateboarder with his board can be modeled as a particle of mass 73.0 kg, located at his center of mass (which we will study in a later chapter). As shown in the figure below, the skateboarder starts from rest in a crouching position at one lip of a half-pipe (point A). The half-pipe is a dry...
  45. K

    How to find center of gravity?

    Homework Statement Find the x- and y-coordinates of the center of gravity of a 4.00 ft by 8.00 ft uniform sheet of plywood with the upper right quadrant removed as shown in the figure below. The dimensions of the cutout are a = 4.30 ft and b = 1.70 ft. I found: xA= 3.7/2 cm...
  46. Y

    Need help with finding Center of Gravity with given radius and height

    Homework Statement Caution: Ignore the weight of the bucket itself. The bottom and the top of a bucket have radii rb = 15 cm and rt = 26 cm respectively. The bucket is h = 36 cm high and filled with water. Where is the center of gravity relative to the center of the bottom of the...
  47. K

    Find Center of Gravity for a Wheelchair

    Hello I was wondering is it possible to figure out the center of gravity for a wheelchair through calculation alone and how is it done? Thanks!
  48. H

    Question about Center of Gravity

    Hi! I am new to the forum. I have a short question: I have uploaded drawings of two "speed boats" with fuel systems. Which boat got the best CG? The one with one, or the one with two fuel tanks? What do you think.
  49. S

    Circular Motion, Center of Gravity, Rotational Motion Homework Help

    I was absent from school for 3 days and my teacher gave this worksheet to me. I have no idea what I'm doing on it. Can anyone please help me with this? Thanks.
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