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. U

    Understanding the Mathematics Behind the Center of Gravity Problem

    I am trying to understand the math for this problem. My instructor did a poor job of explaining it in class. He took a "skyhook" or belt hanger ( looks like a music note make out of wood)" put a stiff belt on it and balanced it on the edge of a table. He exaplained that the center of gravity...
  2. A

    Find the translational kinetic energy of its center of gravity

    A 10.7kg cylinder rolls without slipping on a rough surface. At the instant when its center of gravity has a speed of 11.8 m/s, a) Find the translational kinetic energy of its center of gravity. b) Find the rotational kinetic energy about its center of mass at that time. c) What is...
  3. P

    Centroids and Center of Gravity

    The homoegeneous wire ABCD is bent as shown and is supported by a pin at B. Knowing that l=8, determine the angle theta for which portion BC of the wire is horizontal. Below is the free body diagram with the forces exerted by the pin indicated by the two arrows on the wire. How do I approach...
  4. R

    Understanding Center of Gravity: A Closer Look at Objects and their Balance

    [SOLVED] center of gravity .. hi. i was wondering , is the center of gravity of an object always located in the interior of the object? i think its not because for example, kite has a center of gravity outside its interior of itself right? please correct me and explain to me why this...
  5. M

    Finding the Weight and Center of Gravity of a Heavy Electric Motor

    Two people carry a heavy electric motor by placing it on a light board of length 2.50 m. One person lifts at one end with a force of 400 N, and the other lifts the opposite end with a force of 560 N. a) What is the weight of the motor? b) Where along the board is its center of gravity...
  6. M

    Find Center of Gravity & Horizontal Forces Exerted by Door Hinges

    A door of width 1.10 m and height 1.93 m weighs 290 N and is supported by two hinges, one a distance 0.500 m from the top and the other a distance 0.500 m from the bottom. Each hinge supports half the total weight of the door. Assuming that the door's center of gravity is at its center, find...
  7. L

    Center of gravity in a non uniform gravitational field

    Hi: I have a very big concern about my mechanics homework because a problem says: "Find a formula that gives the position of the center of gravity and make sure that in the limiting case of a uniform gravitational field your formula predicts that both center of gravity and center of mass...
  8. A

    Center of gravity of book overhang

    If you put a uniform block at the edge of a table, the center of the block must be over the table for the block not to fall off. If you stack two identical blocks at the table edge, the center of the top block must be over the bottom block, and the center of gravity of the two blocks...
  9. A

    Resources on center of gravity?

    hey guys, i need some help. we are taking the center of gravity in my physics class, and its all x average = (w1x1+w2x2)divided by negative w... etc... and i really don't get much of it. can anyone recomned a site that might help me?[FONT =Book Antiqua]xxx[/FONT][COLOR =Indigo]xxx[/COLOR]
  10. O

    Calculating the Center of Gravity for a Robot Arm Attachment

    Hello, i am on a robotics team and working on creating a robot to compete at www.usfirst.org competitons. I am having a hard time constructing a formula that will find the ideal center of gravity for our robot arm attachment. here are some specs: length (at the base) 38 in , width 28 in (at the...
  11. S

    Calculating Center of Gravity After Pizza Cut: A Headache?

    hi, here's my question... A pizza has a center of gravity at C, in the middle of the pizza radius = R A smaller circle of pizza is cut from the pizza of radius R/2 at the left side of the pizza so that one the diameter of the hole where the smaller piece was stretches from the edge of the...
  12. quasar987

    Bizzare center of gravity problem.

    Here's the question: "Two equal masses m are separated by a distance a. Find the center of gravity of the two masses relative to a point P on the perpendicular bisector of the line joining them a distance y from the midpoint between them." (perpendicular bisector definition) I never heard...
  13. M

    Solve 850-N Painter's Force on Stepladders

    Hi, I'm kind of stuck on this problem and maybe you guys can help me. If so I greatly apreciate it. An 850-N painter stands 1.20m from one end of a 3.00m scaffold supported at each end by a stepladder. The scaffold weighs 250-N and there is 40.0-N can of paint opposite the painter. How much...
  14. B

    Center of Gravity, objects in eqm

    Hey guys, I was assigned a bunch of questions by my teacher and I'm having trouble with these two: A person is sitting with one leg outstretched, so that it makes an angle of 30 degrees with the horizontal, as the drawing indicates. The weight of the leg below the knee is 44.5 N with the...
  15. C

    Center of Gravity & Rigid-Body Equilibrium Difficulties

    I am having increasing difficulty with the above types of problems. Does anyone know of an easier way to understand the two types of problems?
  16. JasonRox

    Center of Gravity, Non-Uniform Bar

    This is a question I need to do, I'm just going to put an example on what the question is like. In case a teacher of mine comes on here, I know I'm not "cheating". Here is the image: l\ lz.\.../l l...\..../xl l...\______/...l l...l____q_l...l l.....l *Ignore dots. z=56.2...
  17. D

    Center of gravity (it's not center of mass )

    Center of gravity (it's not center of mass!) Hi, I'm a very desperate person right now. For two days (I'm totally dumb) I've been trying to calculate the center of gravity of two rigid bodys... Look, it's not the center of mass (I'm not that dumb!). OK, here's the problem...(at least one of...
  18. L

    What is the Maximum Distance a Boy Can Walk on a Beam Before it Tips?

    hey everybody: here is my problem A uniform, aluminum beam 9.00 m long, weighting 300 N, rests symmetrically on two supports 5.00 m apart. A boy weighing 600 N starts at point A and walks toward the right. How far beyond point B can the boy walk before the beam tips? it will be...
  19. L

    Where is the Center of Gravity for a System of Attached Balls?

    hey all: A ball with radius 0.081 m and mass 1.03kg is attached by a rod of length 4.5 m to a second ball with radius 0.1m and mass 1.94 kg . Suppose the rod is uniform with mass 1.53 kg . Where is the system's center of gravity? Express answer as a distance measured from the center of...
  20. T

    Calculating Center of Gravity with 58% Front Weight: Automobile Problem Setup

    An automobile has 58% of its weight on the front wheels. The front and back wheels are separated by 2 m. Where is the center of gravity located with respect to the front wheels? Need help setting up the problem. Thanks
  21. N

    How Do You Calculate the Center of Gravity for a Carpenter's Square?

    A carpenter's square has the shape of an L, as in Figure P12.7 (d1 = 16.0 cm, d2 = 4.00 cm, d3 = 4.00 cm, d4 = 11.0 cm). Locate its center of gravity. (Hint: Take (x,y) = (0,0) at the intersection of d1and d4) (I tried to attach the picture but I couldn't get it to work, so just know the width...
  22. T

    Where is the center of gravity of this system?

    Two spheres of radius R rest on a horizontal table with their centers a distance 4R apart. One sphere has twice the weight of the other sphere. Where is the center of gravity of this system? Please help me solve this problem.
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