What is Center of mass: Definition and 914 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.

View More On Wikipedia.org
  1. 9

    Center of Mass of a Cubical Box (part c help)

    [b]1. A cubical box has been constructed from a uniform metal plate of neglible thickness. The box is open at the top and has an edge length L=40cm. Find (a)the x coordinate (b) the y coordinate and (c) z coordinate of the center of mass of the box. (part a and b I have solved. I need help...
  2. Q

    Center of Mass. Confused on part b.

    In Fig. 9-39, three uniform thin rods, each of length L = 49 cm, form an inverted U. The vertical rods each have a mass of 14 g; the horizontal rod has a mass of 33 g. What are (a) the x coordinate and (b) the y coordinate of the system's center of mass? (Give your answer in cm)...
  3. M

    Find Center of Mass of Dropped Stones

    A stone is dropped at t = 0. A second stone, with twice the mass of the first, is dropped from the same point at t = 500 ms. (a) How far below the release point is the center of mass of the two stones at t = 850 ms? (Neither stone has yet reached the ground.) (b) How fast is the center...
  4. J

    Velocity of the center of mass

    Homework Statement If a particle of mass 5.6 kg is moving east at 10 m/s and a particle of mass 17 kg is moving west at 10 m/s, what is the speed of the center of mass of the pair? Homework Equations Not sure how it would relate, but to find the center of mass = (m1x1 + m2x2)/(m1+m2)...
  5. G

    Where is the center of mass of the slab

    Homework Statement The figure shows the dimensions of a composite slab; a fraction of the slab is made of aluminum (density = 2.70 g/cm3) and other part is made of iron (density = 7.85 g/cm3). They are not equal as indicated in the figure, but have x1 = 7.5 cm and x2 = 14.5 cm. As measured...
  6. J

    Tipping something given its center of mass? My LAST homework problem

    Tipping something given its center of mass? My LAST homework problem! Homework Statement A rectangular block of mass 3.0 kg is at rest on a table. Its height (in its current position) is 0.7 m, but because its composition varies vertically, its center of mass is at a height of 0.40 meters...
  7. N

    What Determines the Center of Mass Energy in Particle Collisions?

    Homework Statement a. The Hermes experiment is a fixed target experiment. The HERA accelerator creates circulating beams of electrons of energy 27 GeV; these are repeatedly crashed into a target of protons which are at rest. What is the center of mass energy of the electron-proton...
  8. I

    Four momentum of Photon in Center of Mass frame?

    Hi, I have just been pondering the problem of electron - positron annihilation into a single photon in the CM frame. I was stuck at a discrepancy - that in the center of mass frame, the total momentum of the particles was zero, but the energy is the sum of the energies of the original...
  9. fluidistic

    Question about center of mass of a system (human on ice)

    Hello, As I'm seeing the center of mass at university, many questions came to me but I could solve most of them. However I'm not sure about some points. Say you have the system a human on ice. (without air. And consider the ice to be frictionless with the human). I could hardly understand...
  10. S

    Exploring Center of Mass in Physics

    Hi! I'm very curious to know how the Center of mass, that I know from Math is relevant for the physics' subjects. I know already how it affects stars, but I'm interested to know how it is being used in electricity, magnetism, mechanics and other stuff on EARTH :tongue2: Therefore, I...
  11. B

    How far is the center of mass from the handle end of the club-axe?

    Homework Statement A club-axe consists of a symmetrical 11.0 kg stone attached to the end of a uniform 2.9 kg stick, as shown in the figure. The length of the handle is L1 = 93.0 cm and the length of the stone is L2 = 10.0 cm. How far is the center of mass from the handle end of the...
  12. R

    Finding the Center of Mass of a Hemisphere

    Homework Statement Center of Mass of a hemisphere http://www.goiit.com/templates/default/images/chapters/center_mass/image064.gif http://www.goiit.com/templates/default/images/chapters/center_mass/image068.gif Why is volume of elemental disc = Rd\theta (cos \theta) (\pi R^{2}cos^{2}...
  13. D

    Finding Center of Mass for Composite Shapes

    Homework Statement http://docs.google.com/Doc?id=d277r7r_60c2235gfg Homework Equations M(Rcm)=\int(rdm) The Attempt at a Solution Okay, so I've figured out that I have to integrate the radii by the mass element dm, which in this case would be p, because that's the mass/unit area? I think...
  14. T

    Ratio of Kinetic Energies in Center of Mass Frame

    Homework Statement Consider a system of two particles, with masses m1 and m2. What is the ratio of their kinetic energies, T1=T2, in the center-of-mass frame? The Attempt at a Solution I do not really understand the question because center of mass frame was not taught in my class. From...
  15. N

    What is the magnitude of the acceleration of the center of mass

    A constant horizontal force F of magnitude 12 N is applied to a uniform solid cylinder by fishing line wrapped around the cylinder. The mass of the cylinder is 10 kg, its radius is 0.1 m, and the cylinder rolls smoothly on the horizontal surface. (a) What is the magnitude of the acceleration of...
  16. F

    Why does an object rotate about its center of mass when thrown in the air?

    Hello everyone. Take an object in you hands. Throw it in the air. While launching it, your hands will push on the object in different points of it. The object will ALWAYs rotate, free in the air, about an axis that passes for the center of mass. Does anybody know why? I found that in that...
  17. gn0m0n

    Center of mass prob. with sigma notation, vectors

    Homework Statement Prove the magnitude R of the position vector \vec{R} for the center of mass from an arbitrary point of origin is given by the equation M^{2}R^{2} = M\sum{m_{i}r^{2}_{i} - \frac{1}{2}\sum{m_{i}m_{j}r_{ij}^{2} Homework Equations \vec{R} = \frac{1}{M}...
  18. CalleighMay

    Find the mass and center of mass of lamina ?

    Find the mass and center of mass of "lamina" ? Hey guys! I have been on the forum for about a week or so and have compiled a lot of information and techniques to help me understand calculus, so i really appreciate everyone's help! I am a soon-to-be freshman in college and am taking a summer...
  19. D

    Find the center of mass of a semi-circular plate

    Homework Statement Find the center of mass of a semi-circular plate of radius r Find the volume when the plate (above) is rotated around a line along its straight sideHomework Equations 2(pi) integral of r dr The Attempt at a Solution I honestly don't know how to do centroids. :-( I'd like...
  20. Z

    What is the Motion of the Center of Mass in a Billiard Ball Collision?

    Consider two identical billiard balls – one with velocity v and the other stationary. They collide with each other. (a) Describe the motion of the two balls after the collision. (b) Describe the motion of the centre of mass of the two balls before the collision. (c) Describe the motion of the...
  21. D

    Moment of inertia and Center of mass questions

    Hi all, I need some help on a couple questions: 1) Find the moment of inertia about the x-axis of a thin plate of constant density 1 (density = 1) bounded by the circle x^2 + y^2 = 4. Then use your result to find Iy and Io for the plate. Here's how I was thinking to set it up: Since the...
  22. A

    Centroid ( center of mass ) of cardioid revisited

    Centroid ("center of mass") of cardioid... revisited This is actually a variation of the https://www.physicsforums.com/showthread.php?t=119622". As it happens, the cardioid I'm working with is identical to jbusc's: r = 1 + \cos(\theta) and \delta \equiv 1 The task is to find the...
  23. T

    Finding the center of mass by integration.

    Homework Statement Show that the center of mass of a uniform semicircular disk of radius R is at a point 4R/(3(pi)) from the center of the circle. Homework Equations Total mass Center of mass = M rcm = m1r1 + m2r2 + ...The Attempt at a Solution I do not know how to apply integration to this...
  24. T

    Center of mass of a human body

    [SOLVED] center of mass in which direction would the center of mass of the body migrate if the arms were raised overhead? what about if the person had a bilateral amputation of his legs?
  25. A

    How can I determine the center of mass of a vehicle?

    Homework Statement I have to find the center of mass of any vehicle. Homework Equations These are what I have to make. The Attempt at a Solution Here is what I have thought. I have two solutions :- 1. To find the mass of all the major components and their centers and then...
  26. R

    Thin rod suspended freely on end and dropped. KE and Center of Mass

    [SOLVED] Thin rod suspended freely on end and dropped. KE and Center of Mass Homework Statement A thin rod of length 0.75 m and mass 0.39 kg is suspended freely from one end. It is pulled to one side and then allowed to swing like a pendulum, passing through its lowest position with angular...
  27. C

    Find Mass & Center of Mass for a Rod of Length 38.5 cm

    Homework Statement A rod of length 38.5 cm has linear density (mass-per-length) given by the following equation, where x is the distance from one end. λ=50.0g/m+16.5g/m^2 a. What is its mass in g? b. How far from the x=0 end is its center of mass in m? Homework Equations The...
  28. O

    Need to find center of mass of a rod

    [SOLVED] Need to find center of mass of a rod Homework Statement Where is the center of mass of a uniform, L-shaped iron rod of sides X = 0.8 m and Y = 0.5 m, respectively? Take the corner to be at (x,y) = (0,0), with the X and Y sides along those axes, respectively. (Assume that the rod is...
  29. O

    How Do You Calculate the Center of Mass for Multiple Cubes?

    [SOLVED] Finding Center of mass Homework Statement Three cubes, of side 0, 20, and 30, are placed next to one another (in contact) with their centers along a straight line as shown in the figure. What is the position, along this line, of the CM of this system? Assume the cubes are made of...
  30. S

    Center of Mass: Weight Distribution for Bob & Charlie

    Two paramedics, Bob and Charlie, carry a 200 lb patient on an 8-foot-long stretcher. Bob holds the front end of the stretcher and Charlie holds the back end. The patient lies closer to the front end of the stretcher, so his center of gravity is 3 feet from Bob's hands and 5 feet from Charlie's...
  31. B

    Integration Center of Mass Problem -Really frustrated

    Integration Center of Mass Problem --Really frustrated Homework Statement An 800 g steel plate has the shape of the isosceles triangle shown in the figure. What are the x and y coordinates of the center of mass? Homework Equations The Attempt at a Solution I am getting...
  32. L

    Springs, Normal Modes, and Center of Mass coordinates

    [SOLVED] Springs, Normal Modes, and Center of Mass coordinates 1.) Problem The problem of the linear triatomic molecule can be reduced to one of two degrees of freedom by introducing coordinates y_{1} = x_{2} - x_{1}, y_{2} = x_{3} - x_{2}, and eliminating x_{2} by requiring that the center...
  33. C

    Center of Mass of compound cylinder

    [SOLVED] Center of Mass of compound cylinder I have this problem. I have a cylinder filled with two liquids of different densities and not able to mix up (like oil and water). I have to fill the cilynder in such a way so that the center of mass will be located as low as possible. For example...
  34. Z

    What is the relationship between force, momentum, and impulse in a collision?

    A 4.5 kg ball initially rest at the edge of a 2.5 m long, 1.5 m high frictionless table. A hard plastic cube of mass 0.65 kg slides across the table at a speed of 20m/s and strikes the ball to leave the table in the direction in which the cube was moving. At t= 1 sec , F = .5 x10^3 At t= 2...
  35. F

    Center of mass and integrating

    Homework Statement A solid "rough" of constant density (\delta =1) is bounded below by the surface z=4y^2,above by the plane z=4, and one the ends by the planes x=1 and x=-1. Find the center of mass...Homework Equations _{M}xy =\int\int\int z \delta dV Mass = \int\int\int\deltadV then to find...
  36. S

    Center of Mass and Moment of Inertia

    Homework Statement Find the center of mass of the collection of mass points in Figure P.12 and then find the moment of inertia of the system about an axis through the center of mass and parallel to the y-axis. Homework Equations Center of Mass Moment of Inertia The Attempt at a...
  37. S

    Calculating Center of Mass Speed in a Colliding System

    Homework Statement [/B] A loaded coal car with a mass of 120 metric tons traveling at 2 m/s collides and couples with an empty, stationary coal car with a mass of 8 metric tons. (1 metric ton = 103 kg) (c) What is the speed of the center of mass of the system of two cars throughout the...
  38. P

    The Motion of the Center of Mass

    Homework Statement A projectile is launched with speed v0 at an angle theta with respect to the horizontal. At the peak of its motion, it explodes into two pieces of equal mass, which continue to move in the original plane of motion. One piece strikes the ground a horizontal distance D further...
  39. S

    Calculating Center of Mass: Rowboat with Kids | Find x Distance

    When empty, a 166 kg rowboat is symmetrical. A boy of mass 70.5 kg sits 2.1 m from the center of mass of the rowboat toward the front of the boat, and a girl of mass 68.8 kg sits 2.38 m from the center of mass of the rowboat toward the rear of the boat. Find x, distance from center mass of the...
  40. A

    Where Should the Third Particle Be Placed for Desired Center of Mass?

    [SOLVED] Center of Mass problem Homework Statement A 3.12 kg particle has the xy coordinates (-1.76 m, 0.652 m), and a 2.89 kg particle has the xy coordinates (0.380 m, -0.636 m). Both lie on a horizontal plane. At what (a)x and (b)y coordinates must you place a 3.74 kg particle such that the...
  41. P

    The geometric center of the Earth and the center of mass

    Hi all, We are now going to do a kind of experiment in which we use a plumb bob to identify the vertical direction. But I think, the pumb string will point to the center of mass, while we need the geometric center . I mean the COM of the Earth is diffent from the geometric center and it...
  42. N

    Center of mass of concrete wall

    Homework Statement A cylin drical con crete sil o is 4m in diameter and 30m high. it consists of a 6000kg concreet base and a 38000kg concrete cylindrical concreete walls. locate the center of mass of the silo (A) when it's empty and (B) when it is two thrids full of silage whose density is...
  43. L

    Torque, Equilibrium, and Center of Mass

    Homework Statement While standing on a long board resting on a scaffold, a 70 kg painter paints the side of a house. If the mass of the board is 15 kg, how close to end can the painter stand without tipping the board over? http://img146.imageshack.us/my.php?image=physicssl9.jpg Homework...
  44. N

    Finding the final distance of the dog from the shore

    Homework Statement A dog, weighing 11.1lb, is standing on a flatboat so that he is 20.0ft from the shore (to the left in Figure (a)). He walks 8.5ft on the boat toward shore and then halts. The boat weighs 40.4lb, and one can assume there is no friction between it and the water. How far is the...
  45. H

    The z coordinate of the center of mass of the box

    Homework Statement A cubical box has been constructed from uniform metal plate of negligible thickness. The box is open at the top and has edge length L = 97 cm. Find (a) the x coordinate, (b) the y coordinate, and (c) the z coordinate of the center of mass of the box. Homework Equations...
  46. A

    Center of Mass using vectors

    I am looking for a way to find the center mass of an object whose area is enclosed by x^{2} and \sqrt{x} without computing the x and y seperately (a great deal of paperwork). So... M\overrightarrow{R_{cm}} = \int \overrightarrow{r} dm \sigma = \frac{M}{A} = \frac{dm}{dA} \sigma A...
  47. Y

    Finding the Center of Mass of a Human Figure

    Homework Statement (1) the torso, neck, and head (total mass = 42.3 kg) with a center of mass located on the y-axis at a point 0.423 m above the origin, (2) the upper legs (mass = 19.8 kg) with a center of mass located on the x-axis at a point 0.190 m to the right of the origin, and (3) the...
  48. T

    What is the relationship between center of mass and center of gravity?

    Can anyone give me an object where the center of mass and the center of gravity are in different locations?
  49. T

    How Does the Center of Mass Stay Constant When a Child Walks on a Boat?

    I'm not the brightest physics student, so I probably just overlooked something obvious...please help! Problem: A 40 kg child stands at one end of a 70 kg boat that is 4 meters in length. The boat is initially 3 meters from the pier. The child notices a turtle on a rock near the far end...
  50. T

    Center of Mass of an irregularly shaped object

    [SOLVED] Center of Mass of an irregularly shaped object Homework Statement A uniform piece of sheet steel is shaped as shown: ____ | __| | |__ |___| Compute the x and y coordinates of the center of mass of the piece. The sketch above isn't very good but its a graph with an X and Y...
Back
Top