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. Cassis

    B Circular wire center of gravity

    The center of gravity of a circular wire should be in its center? What would happens if we put a marble and a wire into an empty space. Would the gravity force skyrocket as the marble approach the wire center of gravity?
  2. Big Tommy C

    Lifting a mass from a point that is offset from its center of gravity

    Good Evening Everyone. I am having trouble wrapping my head around the physics involved with the example below. At first i was looking at this as if lifting may create a lever of some sort, but I don't believe it has a fulcrum. I am trying to find a formula (if there is one) for lifting a mass...
  3. tivva

    Tipping force and Center of gravity for wall fitted furniture

    Hi All I was wondering if anyone can assist with a task of calculating whether an MDF unit will tip over if fixed only to the wall behind it with mechanical fixings as shown below. And what force will be required to do so. I've given it a try. Let me know your thoughts, would be much...
  4. A

    I If the center of gravity changes on a die, how do the odds change?

    If the center of gravity changes on a die, how do the odds on each of the eyes change?
  5. S

    Engineering Center of gravity and stability of a system

    Suppose I have an object consisting of a hemisphere of radius r and a cone of radius r and height h. The shapes are glued to each other on their faces and the object is set standing on its hemisphere side. Depending on the value of h, the center of gravity for the system will change. I have...
  6. D

    I Questions about center of gravity

    Hello, I am very new to the concept of center of gravity and I have a question. I wanted to know if the center of gravity of an object is always in the same location in 3-D space. For example, if I was able to find the center of gravity for cylinder/rectangle when its lying flat on a horizontal...
  7. G

    Find the center of gravity of a combined cone and cylinder

    Could I please ask for help with the following: Given: The centre of gravity of a uniform solid right circular cone of vertical height h and base radius a is at a distance 3h/4 from the vertex of the cone. Such a cone is joined to a uniform solid right circular cylinder of the same material...
  8. A

    A What are the probabilities of a die with an offset center of gravity?

    With a pure die, all odds are equal. With a pure die, the center of gravity is exactly in the middle of the die. But what if the center of gravity is not in the center? How are the odds then. For example, how do the odds become if the center of gravity is exactly on the line that runs through...
  9. G

    To find the center of gravity of a particular quadrilateral

    Could I please ask for help with the following question. Part 2 is my problem. I have no idea how to begin, any hints would be much appreciated: 1) Prove that the center of gravity of a uniform triangular lamina is the same as that of three equal particles placed at the vertices of the lamina...
  10. J

    Yaw stability -- center of gravity must be ahead of center of pressure

    If we just prove (https://www.physicsforums.com/threads/does-every-object-rotate-around-its-center-of-gravity.998359/) that object don't rotate about CG ,why then center of gravity must be ahead of center of pressure ,for yaw stability? Can you explain physics behind this phenomen?
  11. J

    Does every object rotate around its center of gravity?

    It is said that rocket,plane rotate about center of gravity ,why this is is not case for boats? Boat pivot point is not in center of gravity.
  12. R

    B Why do we need a separate center of gravity idea when we have CoM?

    While deriving the formula for the position vector of the center of mass of a system of ##n## particles, we assume some external force ##\vec{F_i}## on each particle and internal forces ##\vec{f_{ij}}## between any two particles. In the derivation, we come to the conclusion that the position...
  13. K

    I Is space curved at the center of gravity?

    At the core of the earth, or sun, there is no net force of gravity...every direction is up...does this mean that space is not curved, or more generally, becomes less curved from the surface of an object towards its center?
  14. B

    Confusion About Rotational Motion

    I watched a video that showed how to calculate the center of gravity of a horizontal bar suspended from two wires, one attached to each end. Each wire was then attached to a vertical wall. The angle each wire made with the wall it was attached to was given. They treated it as an a example of...
  15. G

    Determing the center of gravity of a shaded section

    Determine the volume of the shaded area around the Y-axis by using the theorem of Pappus Guldinus, where value of R = 143,3 cm. a) Determine the area of the shaded section. b) Determine the center of gravity of the shaded section. c) Detrmine the volume by using the theorem of Pappus Guldinus...
  16. ari-anne

    Finding the center of gravity with torque

    I don't know how to find the center of gravity much less in this problem, so I just created a diagram of the pole with all the forces.
  17. brotherbobby

    Center of gravity and over-hanging blocks

    The red dots show the CM of each block. ##x## is the amount by which the upper block overhangs the lower block. The blue (dashed) line shows the CM of the combination. For maximum overhanging, this line lies on the edge of the table below. By symmetry, the CM lies exactly midway between the two...
  18. Benjamin_harsh

    Is it possible to use the center of gravity to balance a bird toy?

    Here is the picture where person balancing a toy bird with using center of mass. I am bored with center of mass. I want to try same experiment with center of gravity. Is it possible to use center of gravity to balance bird toy ?
  19. brotherbobby

    The Indeterminacy of Problems with Multiple Friction Interfaces

    For convenience, I have marked the C.G. of the sphere as ##G_S## and that of the bar only as ##G_B##. The C.G. of the combination is halfway between them, shown by the green ##G_C##. My answer is that the combination will rotate about ##G_C## (centre of the bar) as it falls. I wonder if I am...
  20. Romka

    I How to determine the center of gravity of a satellite

    Hello, I am trying to find out how to determine the center of gravity of a CubeSat present in an uniform sphere of radius R, using the initial data given by gyroscopes. The satelitte is equipped with magnetometers, gyroscopes, and accelerometers. By taking into account that the only values I...
  21. J

    Rubber Band Car- Wheel Placement and Center of Gravity?

    I have an odd question after making a rubber band car. I'm wondering if placement of my pairs of wheels has any affect on how fast or how far my car goes. It seems to be a very impractical design, but I do want to know the science behind it. My question is if I move two wheels all the way to...
  22. E

    Is Counter-Steering the Only Way to Change Direction on a Motorcycle?

    On a frictionless road and tires, I know the rider wouldn't be able to change the combined center of gravity of the system by moving his weight around. If he pushes the bike to lean to the right, he would go to the left by the amount that would keep the combined cog the same. But a bike with...
  23. P

    Calculating center of gravity of a pole

    Homework Statement A horizontal pole is made of 8 pieces, 1 meter apart each. Forces that do not act at the ends are shown in the picture. The pole does not rotate, and weighs 20N. a. What is the sum of forces applied on the pole? b. Where is it applied? c. What are the forces at the ends...
  24. JustAnotherNewton

    Rotation due to center of gravity

    "The weight of an exercise book in picture A (where the centre of gravity is not on the axis of rotation) rotates so it moves towards the second position in picture B (where the axis of rotation goes through the centre of gravity). Explain why." I don't believe any equations are necessary for...
  25. N

    Center of Gravity and Center of Pressure

    Hello, everyone. This is my first post! Center of gravity does not seem like a difficult concept to grasp, but for some reason, I find it difficult to put into words. Would I be correct in saying: the center of gravity is a point on an object that represents the average position of an object's...
  26. E

    Center of gravity change and acceleration

    Hello Community My first post here so excuse me in case i posted in the wrong place. I basically have to write a paper in school about a physics topic. This includes creating graphs with independent and dependant variables and finding the slope. It should be something to complicated but also...
  27. Zarich12

    B How to find the center of gravity of an object

    Is there a relatively simple way to find the center of gravity of an object? I need to know to see if my model rocket has a high center of gravity. The bulk of he weight is in the bottom.
  28. W

    Center of gravity vs center of buoyancy

    Homework Statement why the floating body still stable when G ( center of gravity ) is above the B ( center of buoyancy)? Homework EquationsThe Attempt at a Solution in my opinion , the statement is worng , because when G is above B , G has the tendency to move downward , causing the object to...
  29. E

    Superposition of Moments of Inertia about Different CGs

    Hi all, You can use superposition to add moments of inertia when they're calculated about the same center of gravity (cg), but let's say you calculate the moments of inertia of several elements of a system about one cg and then use the Parallel Axis Theorem to then reference the total moments...
  30. RLewis42

    Calculating Composite Center of Gravity -- Boat Rack for my Truck

    Hi, I'm new here, great forum! I am building a boat rack for the top of my truck for a particular boat and boat dolly. The boat will be upside down with the beach dolly attached. It is a side loader, so balance is critical. I need to calculate the combined Center Of Gravity (COG) of the boat...
  31. C

    Center of mass and center of gravity don´t match, why?

    For a tapered beam of constant density the center of mass is calculated as the mean of the mass distribution along the central axis, the center of gravity is calculated by getting the equilibrium of the angular moments to the left and right of a fulcrum moving along the horizontal beam. The...
  32. S

    Center of Gravity and Suspension of Object

    Hello everyone, I am trying to understand a center of gravity question regarding an object that is being lifted. I have a part that has a lifting circle that is used to put a hook through to hoist. The part needs to slide onto another part's surface that is about 30 degrees above the...
  33. S

    Calculating the Position of Center of Gravity for a Slender Rod Satellite

    Homework Statement Consider a slender rod satellite in a circular orbit. Show that the position of the center of gravity, ##\rho_G##, can be written in terms of the position of the center of mass, ##\rho_C##, as: ##\rho_G = \rho_C (1+\frac{l^2}{4\rho_C^2})^\frac{1}{4} ##, where ## l## is the...
  34. M

    Center of gravity/moment of inertia

    I am doing a mini hovercraft project. Regarding my design, I plan to place the fan (LIFT) in the middle of a rectangular styrofoam board (15 inches by 8inches). The position of my fan would be (x=7.5, y=4in); this would also be my center of gravity. My origin (coordinate) is at the corner of...
  35. E

    Center of Gravity & Mass: Dist for 2m Rod

    Homework Statement What is the distance between the center of gravity and the center of mass of a vertical rod of length 2 meters, and with a uniform mass distribution? (Center of gravity is defined like the center of mass with weight replacing mass in the formula). Homework Equations nothing...
  36. PrincessIceFall

    How to calculate the height of center of gravity?

    In the above figure, a small weight is placed at 2 cm (0.02 m) from the center of the rectangular prism. Let's call the mass of this small weight (M1) and the mass of the entire body including the small weight (M) Given the dimensions above, I want to know how to calculate the height of center...
  37. M

    Calculating the center of gravity (hard version)

    Homework Statement A Cessna C-172M has empty weight 1350 lbs. When it is weighed, the load on each of the main wheels is 474 lbs. The load on the nose wheel is 402 lbs. Where is the center of gravity of the empty Cessna? Ok so the question assumes you know what a Cessna looks like, but it's...
  38. M

    How Does Adding a Steamer Trunk Affect the Plane's Center of Gravity?

    Homework Statement A partially loaded plane weighs 115,000 pounds. A famous actor's steamer trunk, weighing 300 pounds, is put into the rear cargo hold 250 inches behind the center of gravity. How much does this extra hold shift the center of gravity. Homework Equations W1 = W x (L2 / L) W2...
  39. arpon

    Solve Friction Problem: Find What Happens to A & B

    Homework Statement ##A## and ##B## are two objects with mass ##m_1## and ##m_2## respectively. The floor is frictionless. The kinetic friction coefficient between ##A## and ##B## is ##\mu## ; A constant force ##F## is applied on ##A##. Assume, ##F## is greater than the limiting static...
  40. M

    Understanding Center of Gravity: Exploring the Gravitational Pull of Objects

    The gravitational pull of an object always points toward the center of that, but what makes something an object? If you cut an object in half would each half of the object have a gravitational force toward its center of mass, or would the force point toward the center of mass of the original object?
  41. Z

    Center of mass and center of gravity

    what is the difference between center of mass and center of gravity ? please explain it in an easy way ...
  42. C

    Center of gravity of a 3d triangle using weight

    Hi all, I am after some help to find out how to do the following: I have a triangular object (weighing around 40,000kg) which I can measure and weigh. I have 4 load indicators I can position anywhere beneath the object, these will give me a very accurate reading of the weight of the object at...
  43. P

    Understanding the Center of Gravity: Effects of Mass, Size, Weight, and Density

    Hello everybody I am new here and I would like to ask a simple question about the centre of gravity and how it changes with mass, size , weight , density. etc.etc I would like to understand how this phenomenon happens and I have tried searching online to no avail so please help me understand how...
  44. B

    Calculating Box Stability: An Energy Approach

    Ok I know this should be easy but it's been a few years since my physics lessons at college and I'm stumped. I work in packaging. I'm working on a tool that will tell me if a box will fall over when it is subjected to an edge drop test. That means that a block is placed under one edge of a box...
  45. Abishek

    Center of Gravity - Laws and Explaination

    This is my first thread, and I am excited to post it.:biggrin: My question is that, did any Scientists do any research about Center of Gravity and formulated any laws or gave explanation to it's fundamental behavior? If so, then have they considered the Center of Gravity of liquids and...
  46. V

    Torque and Center of Gravity in Rotating Objects

    Hi ! 2 Objects turn at constant rotational velocity ω rd/s around axis noted "axis" on image (ω clockwise). An external system not drawn force the study to turn at ω rd/s if necessary. From blue object, forces F1 and F2 are applied to orange object. F1 = -F2 in vector. I would like to know if...
  47. H

    How can I determine a vehicle's center of gravity using Euler's equations?

    Homework Statement I need to find a vehicles center of gravityHomework Equations I'm thinking euler's equations but I am new to them.The Attempt at a Solution I'm designing a rig as part of a project that would allow a race car to be suspended from a lift on 4 ropes and then allow to move in on...
  48. S

    Center of gravity of a portion of cylinder

    Attachments Figure # 1 Figure # 2 reproduced from http://www.lmnoeng.com/Volume/InclinedCyl.htmhttp://www.lmnoeng.com/Volume/InclinedCyl.htm Description The blue is the mass inside a cylinder. In steady condition, I would want to know where its Center of gravity point shall be from either of...
  49. C

    Kinetic Moment about the center of gravity

    Hi I need some help explaining kinetic moment and moment of the center of mass. This is an example: http://session.masteringengineering.com/problemAsset/1529176/3/Hibbler.ch17.p107.jpg Okay I know that when you do moment equations: The Moment forces about some point is = to the kinetic...
  50. D

    MHB Center of Gravity Calc: $\bar{y}$

    The y center of gravity is found by \[ \bar{y} = \frac{M_x}{M}. \] In my calculus book, they are always finding the center of gravity of a flat object or objects spaced apart (like planets). Suppose we have a block with length and width \(1\) and height \(a\). On top of this block is another...