Centre of gravity Definition and 73 Threads

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. D

    Where is the Center of Gravity for Various Objects?

    could anyone help to answer the questions below?thank you! 1.where are the c.g and c.m of a uniform circular disk when it is placed in the outerspace? 2.the c.g of a car tyre is adjusted to coincide with its geometric centre .Explain why this is important. 3.some chopsticks have a metal...
  2. P

    Centre of gravity of this system of particles

    Homework Statement Find the centre of gravity of this system of particles Homework Equations attached image showing diagram http://www.zshare.net/image/7209360586277b98/ The Attempt at a Solution Taking moments about a, 4*0+6*30 = 184 then not sure Any help is greatly appreciated Thanks...
  3. A

    Static equilibruim and centre of gravity - HELP

    Homework Statement Hi, Imagine a patient lying down on a bed , you want to weigh her without moving her, but the scale can only support the pair of legs of the bed at one end - or the pair at the other end , but not simultaneously. So he puts the scale at point X (the pairs of bed legs...
  4. A

    Centre of gravity in between two points of different wieght

    Homework Statement Hi, Imagine a patient lying down on a bed , you want to weigh her without moving her, but the scale can only support the pair of legs of the bed at one end - or the pair at the other end , but not simultaneously. So he puts the scale at point X (the pairs of bed legs...
  5. M

    Centroid,centre of mass and centre of gravity

    may i know what is the difference between centroid,centre of gravity and centre of mass of a body?is it necessary that all the points coincide?
  6. J

    What is the center of gravity of a car with passengers on level ground?

    Hi, hope someone can help. I need to find the centre of gravity of a car (x,y and Z). I know the length of the car (5.390m) the distance between the axils (3.116m) and the height of the car (1.515m) I also no the loading on the fronat axil (151.5 N) and the rear axil (111.9 N) and the total mass...
  7. A

    Question about centre of mass and load centre of gravity

    Can anyone tell me that if centre of mass and load centre of gravity of a heavy vehicle doesn't concide,what vl be its effect on vehicles acceleration?
  8. Ed Aboud

    Centre of Gravity: Jump Inside an Earth Cylinder?

    Hi all. I was presented today with a question that I think I know the right answer to but I just want to confirm it. Imagine that a cylinder is removed from the earth, the cylinder being inside the earth, like the height of the cylinder is the diameter of the earth. The cylinder goes right...
  9. N

    Calculating Center of Gravity and Force for a Flagstaff

    Homework Statement This is the case: We going to decide the centre of gravity to a flagstaff with length 10 m We saved up the flagg staff in the thick end. We then need to use a vertical force F in the thin end to keep the flagstaff in horizontal balance. We then saves up the flagstaff in...
  10. S

    How Can I Balance the Center of Gravity in a Model Hovercraft?

    i am presently working on a model hovercraft(prototype).The problem with which i am stuck is that the power supply(battery) i am using weighs around 2.5 kg.My lift motor is to be placed on the center of the hull as it is a rectangular one.Because of this i have to place the battery on one of the...
  11. 6

    How Is the Force Required to Topple a Block Calculated?

    Hi All, If I have block measuring 2m wide by 2m high and 3m long sat on the ground which has a centre of gravity 0.3m from the base how can I calculate the force required to cause the block to topple over. I am trying to calculate wind speed(force) required and how much effect Cog has...
  12. B

    Inertia matrix and centre of gravity of a set of rods

    Homework Statement Three uniform rods OA, OB, and OC, each of mass 3m and length a, lie along the x, y and z axes, respectivley. Show that the inertia matrix relative to Oxyz is Io = 2ma^2 \left(\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right) Determine the inertia matrix with...
  13. K

    Centre of mass vs. centre of gravity

    consider a symmetrical solid body. we say its centre of mass is at its geometric centre. that is, for uniform density we've taken mass to vary exactly as volume. now when the same body is taken from a place of gravitational field A to gravitational field B. say from the Earth to jupiter, this...
  14. C

    Centre of Gravity in a Two-Object System: Calculating with Mass and Height

    Homework Statement A small ball of mass m is dropped at a height of 50 metres. At the same time, a second ball with twice the mass of the first one is launched at an initial velocity of 10m/s from the ground. Where is the centre of gravity in this system? Homework Equations The...
  15. V

    Other Methods of Finding the Centre of Gravity

    Homework Statement I'm doing a coursework on ''Gender differences in whole body centre of Gravity position using the Reaction Board Method of measurement.'' Homework Equations I want to find out what other methods can I use to find the center of gravity so I can put it in my evluation to...
  16. C

    A question about Centre of Gravity

    Homework Statement A uniform disc A of radius 2m is cut as shown in the figure. The cut out is also a disc of radius 1m. O is the centre of gravity of disc A before cutting and O' is its centre of gravity after cutting. Find the distance between O and O' Homework Equations The...
  17. C

    What is centre of gravity. How is it calculated?

    centre of mass There is a mass at a position vector r1 from origin. like wise there are different masses at different r from the origin. the centre of mass is the distance in which the entire mass can be concentrated at some distance R which will give the same EFFECT as that of the...
  18. G

    HELP : Centre of mass and Centre of gravity

    hello , could anyone explain to me the difference between a.) the centre of mass b.) the centre of gravity much aprreciated =) Cheers
  19. B

    Calculating Centre of Gravity of a Lamina: A - B

    Hi, I would like some clarification on the following. Suppose I have a unit square A, symmetric about the xy plane. In addition to this, suppose that I cut a square B from A so that I am left with a lamina (A - B). Where B is a (1/4) * (1/4) square which is symmetric about the x-axis and lies in...
  20. C

    Centre of gravity and dynamics

    in a dynamics problem the example in a book shows a circular rod rotating about a pin at the end. Now the author says that the cg of the rod is at a point and he draws an acceleration vector from cg towards the pin and says that it is the normal acceleration and a perpendicular component called...
  21. M

    How to find centre of gravity for a hemisphere shell?

    How to find centre of gravity for a hemisphere shell?? Can someone show me how to calculate centre of gravity for a hemisphere shell??
  22. A

    Spinning Motion Around Centre of Gravity

    why do bottles or any other things thrown up with a twist always spin about their centre of gravity? Also if all forces pass through centre of gravity of a rocket in space, it will not rotate , even though there is a net moment about any other point except the cg. why
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