What is Centre of gravity: Definition and 73 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. G

    To locate the centre of gravity of a rod

    Could I please ask for a help on how to attack this question? A heavy rod AB of length L can be made to balance across a small smooth peg C when a weight of 2W is suspended from A. Alternatively, it can be made to balance across the peg with a weight of 3W suspended from B. If the distance AC...
  2. G

    To find the centre of gravity of a lamina

    Could I please ask for help with the following: A lamina ABCD is in the form of a trapezium in which DC is parallel to AB, AB = 2a, CD = a and AD = h and the angle BAD is 90 degrees. Find the position of the centre of gravity of the lamina from the edges AD and AB. The lamina is placed...
  3. G

    To calculate the centre of gravity of a spherical cap

    Could I please ask for help as to why I disagree with a book answer on the following question: Answer given is book is $$\frac{1}{2}(a+b)$$ Here's my proposed method: Prior to this question there is an example of a similar question: And here is the answer: So, to solve my question I...
  4. T

    Defining the Centroid, Centre of Mass, Centre of Gravity for 2D/3Dshapes

    Homework Statement: Defining Centroid, Centre of Mass, Centre of Gravity for 2D/3Dshapes Homework Equations: Defining Centroid, Centre of Mass, Centre of Gravity for 2D/3Dshapes Hello all; I am trying to understand the terms:- - Centroid for a 2D shape and 3D shape - Centre of Mass for a 2D...
  5. Benjamin_harsh

    Centre of gravity shifted to what position?

    A square sheet of metal has a square of one quarter of the original area cut from one corner as shown in the figure. Which of the following statements is true about the position of the centre of gravity of the remaining portion of the sheet? a) center of gravity lies at a distance of 5/12 of...
  6. T

    Difficulty understanding Centre of Gravity

    Hey, This isn't a homework question I need help with but more of a concept I can't seem to grasp. I understand that Centre of Gravity is: the point on a body where all the weight can be considered to act. And I understand how to find this point on different types of bodies. However, this...
  7. John Mohr

    I Technique to find CG seems like should be for C.M. instead

    When thinking over the method of finding the centre of gravity that Julius Sumner Miller shows in this classic video, I wondered about if it would work in some other extreme situations. Imagine a uniform, continuous plank of length equal to 1 Earth radii positioned at the surface of the Earth...
  8. Raghavendar Balaji

    Centre of gravity of a 3D irregular object

    Homework Statement A complex or irregular body with some mass, m. How to determine the 3 co-ordinates of centre of gravity? Homework Equations Moment method with ∑M = 0. The Attempt at a Solution Say I have a gearbox and I need to find the COG. I can mount the gearbox at two longitudinal...
  9. J

    I Centre of Gravity: How Can This Be Possible?

    Hi... The centre of gravity is the point where the whole weight seems to act on. How can this be possible? Ty in advance
  10. M

    I Reduction of the Centre of Gravity

    Hi, I'm trying to figure out the equivalent change of the Centre of Gravity when an amount of liquid is reduced. This could be a fuel oil tank on a ship. In other words, if I e.g. reduce the content what would be the equivalent vertical change of Centre of Gravity on a ship with a total...
  11. DevonZA

    Centre of gravity, moment of inertia and radius of gyration

    Homework Statement Homework Equations Centre of gravity: X=m1x1-m2x2/m1-m2 MOI rectangle: 1/3ml^2 MOI triangle: 1/18md^2 Radius of gyration: Ixx=mk^2 The Attempt at a Solution Mass of body 1: b*l*p = 0.8*1*10=8kg Mass of body 2: 1/2b*h*p = 1/2(0.4)*0.6*10=1.2kg1.1 X=m1x1-m2x2/m1-m2...
  12. C

    I How to Calculate an Offset for Centre of Gravity using Weight and Distance?

    Hi, I have a software application which calculates the CoG of an item when it is placed on to four weighing indicators. It calculates the CoG using the weight and distance between weighing points and provides the output as an X and Y co-ordinate of the object. What I would like to do is...
  13. Poetria

    Centre of gravity, centre of buoyancy (image)

    Homework Statement The first image: Without information on the interior construction of the boat or the mass distribution of the exterior shell of the boat, which of the following points can be the boat's center of gravity? The second image: Our boat from the previous question is now...
  14. R

    Effect of Lowered Center of Gravity on Jumping Time

    Homework Statement Homework EquationsThe Attempt at a Solution For part a) I got t=0.571 seconds For part b) I got s=4.6m But part c) is what I'm stuck on. If his centre of gravity has shifted lower by 50cm, is his time spent in the air greater?
  15. S

    What is the Difference Between Gravitational Force and Weight?

    Homework Statement Centre of gravity - the point at which: 1) gravity acts on a body or 2) weight of a body may be considered to act. The answer is 2) and I understand why - because gravity acts all over but it is easier to calculate a single point, an average point of where the mass is...
  16. Shafia Zahin

    B Differences between Centre of Gravity and Centre of Mass

    Hello, I need help in understanding the concept of centre of gravity and centre of mass.I really get confused in the two of these.It is written in books that the centre of gravity is never changed in an object,its position is constant.But as far as I know the position of an object determines the...
  17. I

    How do I find the centre of gravity of this object?

    Homework Statement Hi everyone, I need help finding the centre of gravity for this object in order to find its stability in water. However, I am having trouble finding out the centre of gravity. Homework Equations N/A The Attempt at a Solution [/B] The answer says that it is 1, but...
  18. N

    How distance from CoG affects acceleration over time

    Let's say an object is falling towards Earth from a long distance away. As it gets closer and closer, the acceleration would increase, inversely proportional to the distance squared. Is there any way I can graph this on an acceleration/time graph, or a distance/time graph? The challenge is...
  19. avito009

    Whats the relation between the centre of gravity?

    Whats the relation between the centre of gravity of a structure and the middle third rule?
  20. M

    Difference between centre of mass and centre of gravity

    Homework Statement Now, I know the centre of gravity can change depending on how close to uniform the gravitational field is, and it is where the weight appears to act from. But, what is the centre of mass? Ok, it is a constant; doesn't change; and in an uniform gravitational field the two...
  21. R

    Load rotating device - will it slide?

    Homework Statement I'm designing a device for changing a load position from vertical to horizontal. It has a wheeled frame (2) which allows an operator to transport the load after reorientation. The combined centre of gravity of a rotating platform (1) and the load moves forward due to...
  22. D

    Centre of Gravity and Centroids

    Homework Statement http://puu.sh/lJgzB/5b877de108.jpg http://puu.sh/lJgAR/c28393f051.jpg Can someone please explain these two slides to me? Especially the first one, It seems to be summing the Moments in y and Moments in x. The sum of the moments in y is xW. I understand that but then it...
  23. andyrk

    Why does the centre of gravity shift when a rod is displaced?

    In the first attachment, the normal reactions are equal. But when the rod is displaced a slight distance x towards the right (second attachment), the normal reactions change to R1 and R2 with R2 being greater than R1. Why is that?
  24. M

    CG location effect for steady state cornering

    I am having trouble understanding this. The question was how to limit breakaway oversteer I know that putting the CG to the rear will increase the rear traction and induce understeer as there is less grip on the front tyres. However, I have also found that to reduce oversteer you want to...
  25. D

    Modal Analysis of a Rotor Blade Using Simpack

    Hi everyone, I am relatively new to Simpack and would appreciate some help with getting started. Basically I am trying to obtain the displacement of a rotor blade as it rotates (I already have the model). I want to have the displacements of each modal shape along the entire blade radius. Now...
  26. A

    What is the Optimal Position for a Spanner to Achieve Balance and Stability?

    The attached file contains a question my brother asked me solve. But this problem might have some problem of its own. I feel like every position of the spanner is a probable one. Can someone please help. p.s. i know the answer but avoiding giving it to avoid getting biased.
  27. PrincessIceFall

    Review centre of gravity calculation

    <<Mentor note: Thread merged with duplicate from other forum.>> Half an octagonal prism. A small weight is placed 2 cm from the centreline of the vessel. The rod on which the weight is on is placed at (L/2) i.e at the center of the length of the vessel. The height of center of gravity from the...
  28. C

    Calculate Centre of Gravity/Mass of Non-Uniform Objects Using Load Cells

    Hi, I need to calculate the centre of gravity/mass of a non uniform object. The setup will be using load cells to measure the weight of the object in moveable positions. If you imagine an object being lowered onto 3 points, the weight reading at each point can be measured individually. But...
  29. aab234

    Centre of gravity for multiple objects

    Hi. This is my first post so apologies if I do anything wrong. I have a homework question. *calculate the distance of the centre of gravity from support A for a framework containing 4 crates at 52kg per crate. I'll describe the diagram: A is on the far left. 3m from A are 2 crates stacked...
  30. D

    Equation for Centre of Gravity of a Hollow Conical Frustum

    Homework Statement I would like to find a general equation for calculating the centre of gravity (COG) of a hollow conical frustum. Homework Equations Consider a solid conical frustum as shown below: The COG of this shape may be derived as follows: COG =...
  31. K

    Centre of gravity of a car shifting with speed

    Hi. I have heard that with high speed of a car, its centre of gravity (CG) shifts backward. Isn't the CG a function of mass and dimension? Pl. explain. Thanks.
  32. C

    Confusion in centre of gravity and centre of mass differentiation

    Hi friends, I have Kinetic energy problem during collision. Please Help me in solving this. Thank you all in advance. The problem is as: https://fbcdn-sphotos-c-a.akamaihd.net/hphotos-ak-frc1/q71/s720x720/1380301_1432382870322152_49372184_n.jpg Attempt...
  33. I

    Discussion for Centre of Gravity of an irregular shaped object(Lamina)

    Hello, can someone tell me a discussion for one of my physics labs? Aim: To determine the centre of gravity of an irregular shaped object which is a lamina. Apparatus: Cardboard, Pendulum bob, string, retort stand, Pin, Cork, Pencil. I have already determined the results and all i need is...
  34. D

    The net force and centre of gravity of a one dimensional object

    I have been trying to derive a formula for the forces acting on and the centre of gravity of objects in a one dimensional space. I've started in one dimension to make things easier and intend to move on to two dimensions soon. I tried to do it without referring to any source and I got a solution...
  35. V

    What is the center of gravity for different shapes in blanking calculations?

    what is the centre of gravity of an arc(as opposed to sector) and that of the periphery of triangle(not the area of the triangle)? I'm supposed to use it for calculating blank diameter before drawing and for calculating centre of pressure during blanking.
  36. G

    Discovering the Centre of Gravity: Tips and Techniques for Finding Balance

    Hello I am stuck on this question here(in attachments ) How do you find the centre of gravity ?
  37. S

    Centre of Gravity and Centre of Mass

    Hey folks, I was doing some moments problems the other day, and I started considering centre of mass and centre of gravity and have gotten myself rather unsure. My textbook defines centre of mass as "the point through which a single force has no turning effect", which I have an intuitive grasp...
  38. O

    Torque (of a couple) and centre of gravity MCQ

    Homework Statement Homework Equations I know torque of a couple = One of the forces x the distance between the 2 forces. The Attempt at a Solution I don't know how to approach this blasted problem. Any help would be very much appreciated.
  39. D

    Centre of gravity of a submerged body?

    Hi guys, I can't get my head around the centre of mass of a submerged body at all. the notes I've been given don't actually state how you calculate the centre of mass of the submerged body at all and just state it with no decernable pattern. I did assume that it was the centre of mass of that...
  40. J

    Distance of the centre of gravity

    Homework Statement Calculate the distance of the centre of gravity from the support A Homework Equations one crate = 3000N The Attempt at a Solution Anyone know how to start?
  41. A

    Centre of mass and centre of gravity

    Hi,today my teacher said that there is a little bit different between centre of mass and centre of gravity. But he said there is no different between them in my level(teenager) What is the different between them and why we can ignore the differences?
  42. B

    Centre of Gravity: Explaining Concepts & Examples

    Hi, I am just wondering if someone can help explain a concept of CG: I understand that in a homogeneous object the CG is in the geometric centre In a object without a constant mass, the CG will be towards the end with the greater mass But it say in my textbook that: "It is also possible...
  43. I

    Calculating Centre of Mass and Centre of Gravity for a Humanoid Robot

    hii.. this is shruti... i want to make an inverted linear pendulum of bi ped humanoid robo... can any 1 help me in calculating the centre of mass and centre of gravity... of a humanoid robot...
  44. J

    Centre of Gravity of Multiple Crates

    Homework Statement After a period of time the frame contains four crates. Calculate the distance of the centre of gravity from the support A.Homework Equations The weight is 200KG per crateThe Attempt at a Solution I know how to calculate the centre of gravity but this problem is stupid...
  45. F

    Force to topple a block. (moments, centre of gravity)

    Hi I would greatly appreciate help on this problem. Homework Statement Ok so here is the problem Homework Equations The Attempt at a Solution I first tried to work out the moments for the block on the ground with no angle to the ground. moments about a = .45(35000*g) -...
  46. B

    Centre of gravity calculations

    Hello all, just a little centre of gravity question: A 1.7m long barbell has a 20kg weight attached on its left end and a 35kg weight on its right end. a) If you ignore the weight of the bar itself, how far would from the left of the barbell is the centre of gravity - I had no trouble...
  47. A

    Image processing centre of gravity

    what is the centre of gravity of an image in image processing ?
  48. S

    Is the centroid always the centre of gravity for a triangle of uniform density?

    Centroid...centre of gravity! How to prove that centroid is the centre of gravity of a triangle...
  49. Z

    Buoyancy and Centre of gravity

    Homework Statement A thin wooden plank 1m long is kept on the protruding stone with some of its part immersed in water. Will the centre of gravity of the wooden plank be inside the water or outside?Homework Equations The Attempt at a Solution For the wooden plank to be in equilibrium, moments...