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. M

    Center of Gravity of a Hiker and Backpack

    Homework Statement An 80 kg hiker carries a 20 kg pack. The center of gravity of the hiker is 1.1m above the ground when he is not wearing the pack. The center of gravity of the pack is 1.3m from the ground when it is worn. How far above the ground is the center of gravityof the hiker and...
  2. B

    Torque and center of gravity problem

    First off, here's the problem: Suppose your lab partner has a height L of 173 cm and a weight w of 715N. You can now determine the position of his center of gravity by having him stretch out on a uniform board supported at one end by a scale. If the board's weight is 49N and the scale reading F...
  3. M

    Center of Gravity and probability

    Greetings! I'm new to the forum. I am a math major with a concentration in probability. A relative wants me to find the center of gravity of the pipe. I attached a diagram below. I have no clue how to find it. I have never seen anything like this before. I know that you integrate over the...
  4. L

    How Does Dancer Movement Affect the Center of Gravity on a Dance Floor?

    Homework Statement Given: A flat dance floor of dimensions ℓx = 19 m by ℓy = 23 m and has a mass of M = 1600 kg. Use the bottom left corner of the dance floor as the origin. Three dance couples, each of mass m = 150 kg start in the top left, top right, and bottom left corners. What is the...
  5. J

    Find Center of Gravity of 3D Objects to Balance in Water

    To find the center of gravity of a 3-D object? The problem is to balance a body in water so that it moves in a straight line when propelled. As the weight distribution in the body is not even it is tilted to one side and when propelled tuns in the direction of tilt. How can the body be made to...
  6. S

    Finding Center of Gravity in a 4-Object Arrangement

    Homework Statement Consider the following mass distribution where the xy coordinates are given in meters: 5 kg at (0.0, 0.0) m, 3 kg at (0.0, 4.0) m, and 4 kg at (3.0, 0.0) m. Where should a fourth object of 8 kg be placed so the center of gravity of the four-object arrangement will be at...
  7. K

    Center of gravity of a stack of coins

    Homework Statement A penny has a mass of 2.5 g and is 1.5 mm thick; a nickel has a mass of 5.7 g and is 1.9 mm thick. If you make a stack of coins on a table, starting with five nickels and finishing with four pennies, how far above the tabletop is the center of gravity of the stack...
  8. G

    Finding the center of gravity & mass by torque?

    I don't know how to do these kinds of problems; I just need an example of one, could someone just work it out with an explanation? Feel free to change the values or whatever. This particular problem isn't to turn in, I'm studying for a test on this material. A meter stick is pivoted the...
  9. G

    Center of gravity & mass of a nonconformed meterstick

    A meter stick is pivoted the 50-cm mark but does not balance because of nonconformities in material. 150 g and 200 g weights ar placed at the 10-cm and 75-cm marks to balance the meterstick. When the weights are interchange, the pivot point is at the 43-cm mark. find the mass of the stick...
  10. C

    Center of Gravity of a Triangle Proof

    Homework Statement The "center of gravity" of the triangle with vertices at A, B, and C is the point 1/3(A+B+C). Show that the center of gravity of a triangle is always the same as that of the triangle formed by the midpoints of its sides. Homework Equations The Attempt at a...
  11. O

    Tennis racket center of gravity

    If I have a tennis racket, and I add weight to its handle, would it make the tennis racket more maneuverable? the swing weight of the racket would not change, in fact the weight would make the racket heavier. but the weight would move the center of gravity towards my hand.
  12. R

    HELP Simple center of Gravity problem

    2) A Uniform Boars has a mass of 1.5kg and length of 100cm, Note the Weight is negligible. A) Where should it be supported so that it will balance a 10g mass places at an end, a 60kg mass on the other end, and a 40kg mass placed 30 cm to the 10g mass? The answer should be 0.511m a...
  13. A

    Center of gravity/ weight distribution

    Honestly I know I'm right as far as what I said in a conversation regarding the effects to the mechanical components we were discussing. Basically all I'm looking for is someone to look at how I explained the physics and if there is a better way to explain this to them because its not sinking...
  14. A

    Center of gravity vs center of mass

    Is it different from the center of mass? My book says yes but doesn't answer the question.
  15. C

    Two rigid bodies combined center of gravity

    Hello all. I'm trying to find the equation for combined Center of Gravity (CoG) when you combine two objects with different weight. I know how to find the centroid, which is what the CoG would be if both objects were the same weight. But what about two objects with different weight...
  16. R

    Center of gravity calculate force on tail

    Homework Statement The fore and aft distance between the two main wheels and the single tail wheel of an aircraft is 8m. The unloaded weight of the aircraft is 20kN and its centre of gravity is 0.5m behind the main wheels. Calculate the force on the tail wheel and on each main wheel...
  17. S

    How Does a Student's Position Affect Scale Readings and Center of Gravity?

    Homework Statement For some reason I can't get my picture to show up, but here is the link to it: http://img.photobucket.com/albums/v302/Robi41035/Picture1.jpg "The plank is uniform and 2.2 m long. Initially the scales each read 100 N. A 1.60 m tall student then lies on top of the...
  18. X

    How Do You Calculate the Overall Center of Gravity for a Person?

    Homework Statement a person is standing on a level floor. His head , upper torso , arm , and hand together weigh 438N and have a center of gravity that is 1.28 m above the floor. His upper legs weigh 144N and have a center of gravity that is .760 m above the floor. Finally, his legs and feet...
  19. B

    How Can I Find the Center of Gravity for a Uniformly Distributed Mass?

    Homework Statement i need to find the center of gravity of the attached shape Homework Equations i know that in order to find center of gravity i can use the equation \Sigmamixi/\Sigmami but for the case it doesn't work becasue i don't have mass of this shape it just says that the mass...
  20. J

    What is the Distance from C to C' for a Circular Pizza with a Piece Removed?

    Homework Statement A circular pizza of radius R has a circular piece of radius R/2 removed from one side. Clearly the center of gravity has moved from C to C' along the x-axis. Show that the distance from C to C' is R/6. (Assume that the thickness and density of the pizza are uniform...
  21. Saladsamurai

    Trying to Find Center of Gravity on Semi Truck (a real one)

    Trying to Find Center of Gravity on Semi Truck (a real one)! Homework Statement For one of my classes I have to prove, using very basic physics, that a scene from a movie is very unrealistic. So my group chose the "truck flip scene" from Batman Dark Knight. I am desperately searching to...
  22. O

    Z coordinate of the center of gravity

    Hey, for this problem i need to find the z coordinate of the center of gravity. I have a cylinder/disk whose height is along the y-axis and radiates about the x and z axis. what is the equation to find z bar. this is just one part of the problem.
  23. L

    Determine the distance of the center of gravity from the end X of the plank?

    Homework Statement A non-uniform plank of wood XY is 2.50m long and weighs 950N. Force-meters (spring balances) A and B are attached to the plank at a distance of 0.40m from each end, as illustrated in the Figure below http://img266.imageshack.us/img266/2377/physicsp23bgh5.png [/URL] When...
  24. B

    Center of Gravity for nonuniform plank

    Homework Statement A box of negligible mass rests at the left end of a 1.90m, 23.5kg plank The width of the box is 75.0 , and sand is to be distributed uniformly throughout it. The center of gravity of the nonuniform plank is 50.0 from the right end. I am lost pls help me i know the...
  25. I

    How Much Sand Is Needed to Balance a Plank Horizontally?

    Homework Statement A box of negligible mass rests at the left end of a 2.00-m, 25.0-kg plank (see image). The width of the box is 75.0 cm, and sand is to be distributed uniformly throughout it. The center of gravity of the nonuniform plank is 50.0 cm from the right end. What mass of sand...
  26. T

    Rigid Objects in Equilibrium & Center of Gravity

    [SOLVED] Rigid Objects in Equilibrium & Center of Gravity Homework Statement http://img149.imageshack.us/img149/8568/0968lr6sc4.gif A lunch tray is being held in one hand, as the drawing illustrates. The mass of the tray itself is 0.220 kg, and its center of gravity is located at...
  27. V

    Where is the Center of Gravity of a Lying Person?

    Homework Statement A 160cm tall person lies on a light(massless) board which is supported by two scales , on under the feet and the beneath the top of the head. the scale under his feet read 29.4kg and the scale under his head reads 32.8 kg ... where is the center of gravity of this...
  28. I

    Center of gravity: Really confused (HW problem)

    Center of gravity: Really confused Hi everyone, My question is: Find the center of gravity for the board below: Assume that the board is uniform in thickness and that the hole in the plate is centered from top to bottom: I only know that you have to find the area of the circle and the board...
  29. W

    How Far Can a Person Walk on an Overhanging Plank Before It Tips?

    Homework Statement A uniform plank of length 4.6 m and weight 210 N rests horizontally on two supports, with 1.1 m of the plank hanging over the right support. To what distance x can a person who weighs 448 N walk on the overhanging part of the plank before it just begins to tip? Homework...
  30. S

    Center of gravity of an irregular object of mass

    The center of gravity of an irregular object of mass 4.50 g is shown in the figure. You need to move the center of gravity 2.00 cm to the left by gluing on a tiny 1.60-g mass, which will then be considered as part of the object. Where should you attach this additional mass? Express your answer...
  31. D

    Where Is the Center of Mass for Three Aligned Meter Sticks?

    Homework Statement Three uniform meter sticks, each of mass m, are placed on the floor as follows: stick 1 lies along the y-axis from y = 0.500 m to y = 1.50 m, stick 2 lies along the x-axis from x = 0.110 m to x = 1.11 m, stick 3 lies along the x-axis from x = 1.34 m to x = 2.34 m...
  32. B

    Mountain climber - center of gravity, tension, angles

    Homework Statement A mountain climber is rappelling down a vertical wall (the figure below ). The rope attaches to a buckle strapped to the climber's waist 15 cm to the right of his center of gravity. If the climber weighs 770 N, find (a) the tension in the rope and (b) the magnitude and...
  33. T

    Finding normal force from center of gravity

    Homework Statement The figure shows a person whose weight is W = 725 N doing push-ups. Find the normal force exerted by the floor on (a)each hand and (b)each foot, assuming that the person holds this position. Homework Equations center of gravity = cg Xcg = (W1x1 + w2x2 +...)/(w1 +...
  34. J

    Calculating Center of Gravity for Shape T: 60mm x 6mm

    Homework Statement Center of gravity for a shape T both arm are 60mm long and 6mm wide. Homework Equations dont know the equation but seeing as there is not wieght involved am guessing the formula isn't that hard. a discription of the formula and how to use it would help alot...
  35. B

    Center of Gravity: Rod Kicked Quickly - What Happens?

    Homework Statement My friend's little brother took some physics test a week or so ago, and he was asking about some of the questions that were on it. This was one of them: There is a rod (uniform density, mass) which is balancing on the ground on its end (It basically looks like a flag pole)...
  36. C

    Find Center of Gravity Distances for Cut Discs

    Homework Statement A unifrom disc A of radius 2m is cut as shown in the image. The cut out is also a disc of radius 1m. Find the distance of the two center of gravity before and after the paper disc is cut. http://crossfacer.com/circle.jpg Homework Equations x=m1x1/M+m2x2/M+... The...
  37. S

    Center of Gravity - Product Safety Question

    Homework Statement Hi. I am a product designer and I'm looking for a way to solve the following: I have a toy bin (see jpeg) which currently does not pass a child safety test as it tips over under certain conditions and I need to change the dimensions so that it will pass this test...
  38. G

    Where is the center of gravity of this person

    1. A 160 cm tall person lies on a light (massless) board which is supported by two scales, one under the feet and one beneath the top of the head. The scale under the feet reads 29.4 kg and the one under the head reads 32.8 kg. Where is the center of gravity of this person measured from the...
  39. D

    Center of Gravity: Where Does it Lead?

    I was wondering, center of gravity is the point in the object where other objects are pulled to. (they want to get to the center, but the onject itself is stopping it, like we won't fall to the center of the earth, because the eart itself are stopping us.) Anyway, let's assume that. What if...
  40. P

    Equilibrium and Center of Gravity problem

    I'm having some trouble finding a definitive answer for this problem of my physics lab. The large quadricep muscles in the upper leg terminate at the lower end in a tendon attached to the upper end of the tibia. The force on the lower leg when the leg is extended are modeled below (attached...
  41. T

    Force and Torque or Center of Gravity ^^

    :rolleyes: I think I'm getting pretty good at my free body diagrams.. at least I hope so... Well, in any case, I'm having trouble with my homework problem again X_X (specificially c, because it's new). I was wondering if someone could check my work because on problems that are assigned before...
  42. Y

    Err, two questions related to center of gravity and friction

    "since the distance of forces(the center of gravity forces) from the gravity are at a very large distance so they are just like parallel forces" now what do parallel forces have to do with distance or vice versa? Explain. and then please explain the friction of sand. anyone?!
  43. C

    Center of Gravity Question: Pretty Tough Conceptually

    THANKS FOR THE HELP! i solved the problem successfully (correct answer too)
  44. W

    Why Is the Center of Gravity Calculation Resulting in Negative Coordinates?

    Hello, I with this problem, I am getting the correct answer, but I do not know why the book's answer is negative: "Consider the following mass distribution: 5.00 kg at (0,0) m, 3.00 kg at (0, 4.00) m, and 4.00 kg at (3.00, 0) m. Where should a fourth object of mass 8.00 kg be placed so...
  45. H

    Rigid Objects in Equilibrium and Center of Gravity

    Thanks in advance-- Problem: A woman who weighs 470 x 10^2 is leaning against a smooth vertical wall, as the drawing shows. a) Find the force FN (directed perpendicular to the wall) exerted on her shoulder by the wall. b) Find the horizontal component of the force exerted on her shoes by...
  46. S

    Lifting Jet Engines: Rigging Cranes for Complex Objects

    Ok If you had a complex object, like a jet engine and what to rig a crane correctly to pick it up, what would be a good procedure on how to go about this? Let's say you had access to the engineering drawings and such, and could thus get approate weights for subsystems(turbine, bypas fans, etc...
  47. M

    Center of gravity and the center of mass

    :cry: been wonderin' for an hour already nac somebody please answer if there is a difference between the center of gravity and the center of mass if there is, what is it?
  48. G

    Center of Gravity: Finding 0.387m from 1kg Sphere?”

    i can get the answer i should for a ball with radius 0.0800m and mass 1.00kg is attached to a rod 0.400m long in length to a second ball with radius 0.100m and mass 2.00kg. Where is the center of gravity of the system. i used the formula Xcg = (M*R + m*r)/(M+m) and get an answer of 0.093 but...
  49. A

    Where is the Center of Gravity of a Car Located?

    Find the center of gravity of a car with respect to the front axle. There is a distance of 130 inches between the front and back axles. There is a force of 1800lbs on the back axle and 2100lbs on the front axle. I changed 130 inches to meters and I got 3.30m. I changed both 1800lbs and...
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