Center of mass Definition and 916 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. E

    Rapiditiy and center of mass energy

    Hey Folks, i just wondered if there is a direct connection between the rapidity parameter y and the center of mass energy squared s (for example in the case of two colliding massless particles (aka high energy approx). I tried googling it, but failed to find any satisfying answer. Thank...
  2. Y

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  3. M

    Adjusting Center of Mass for Equal Weight Objects

    [The subject should say "adjusting center of mass"] Hello, I am trying to make a machine that "pairs" two object's center of mass and weight. I was trying to figure this out myself but with barely primary school completed, I obviously could not figure it out. Any help is very much appreciated...
  4. S

    Solving for Center of Mass in a Bent Wire: xcm and ycm Values Explained

    A wire of uniform density is bent into the shape shown in the figure below. The value of L is 0.740 cm. Answer the following questions assuming that the origin is at the bottom left corner. What is the value of xcm? cm What is the value of ycm? cm Attempt xcm = 2*.74 = 1.48...
  5. M

    Finding Center of mass and Moment of inertia Experimentally.

    Hi, I am doing a science experiment. For that, I have made a small structure (sort of, almost pyramid like) using metal strips. I have calculated mathematically: its center of mass/gravity, moments of inertia matrix and principle MI axis ( usual formulae). My job first is to find these same...
  6. K

    Having trouble finding the center of mass for multiple objects

    Homework Statement Find the x-coordinate of the center of mass of the composite object shown in the figure. The sphere, cylinder, and rectangular solid all have a uniform composition. Their masses and dimensions are: sphere: 200 g, diameter = 10 cm; cylinder: 450 g, length = 11 cm, radius =...
  7. P

    Find the center of mass with tripl-integral

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  8. T

    Momentof inertia and center of mass

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  9. edpell

    Is the Inertial Frame Defined by the Universe's Center of Mass Unique?

    Isn't the inertial frame defined by the center of mass of the universe somehow special? To get to any other frame an object must experience a force and be accelerated to a new velocity. In this case the CMB shows us the inertial frame of the CM of the universe. I understand that velocity is...
  10. Y

    Conservation of linear momentum & center of mass

    Homework Statement Two cars are driving along the road at constant speeds V1, V2. At t=0 they begin to accelerate with constant acceleration a1, a2. Under what circumstances is the center of mass frame of reference inertial?Homework Equations Fext=0 ==> change in momentum=0The Attempt at a...
  11. M

    Conservation of linear or angular momentum + center of mass.

    So I have been reading about conservation of linear momentum and conservation of angular momentum of a rotating object. For example a thin rod resting horizontally on the a flat surface. If this rod is being hit by a small object(collision), the rod will rotate about it's center of mass and will...
  12. A

    Center of Mass and Mass Moment of Inertia

    Homework Statement Using masses, springs a stop watch and ruler, determine the location of the center of mass and mass moment of inertia about an axis passing through the center of mass of a bicycle crank. The Attempt at a Solution I've been staring at this problem for a while now...
  13. X

    Find Center of Mass: Calculate x,y Coordinates with R = sum(m*r)/sum(m)

    1. The density of part A (p)(kg/m^3) and in part B (p/2)(kg/m^3). Find the coordinate (x,y) of the center of mass of this object. (consider a piece of the object that is one meter in the z direction) 2. R = sum(m*r) / sum(m)...maybe? I am completely stumped on how to start this problem my...
  14. B

    Understanding Center of Mass: Common Misconceptions Explained

    so I am not too sure how to answer a question... ill word it the best i can: While doing an experiment where we use a Plumb Line and paper object and find the center of mass by letting the string (with mass attached to other end) hand and draw lines that eventually intersect at on specific...
  15. G

    Finding Center of Mass and Velocity of Three Moving Balls

    Three Balls are moving along a straight line having the instantaneous positions shown in figure 8.15. At that instant, find the location and velocity of the center of mass of this system. Figure 8.15 Mass A---------------------Mass B-----------------------------------Mass C...
  16. T

    Translational Motion and Center of Mass

    Homework Statement A 280-kg flatcar 25m long is moving with a speed of 6.0m/s along horizontal frictionless rails. A 95-kg worker starts walking from one end of the car to the other in the direction of motion, with speed 2.0m/s with respect to the car. In the time it takes for him to reach the...
  17. S

    What is the Height of the Cone in Terms of r?

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  18. D

    When Can You Pretend All the Mass is at the Center of Mass?

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  19. T

    Rigid body solid: center of mass and tendency to topple

    Homework Statement A whimsical piece of furniture has the base shaped like a star. Formulate the condition in terms of the location of the center of mass of the object that the piece would not topple over. A sketch would be helpful. The Attempt at a Solution Can someone help me...
  20. J

    Center of Mass of draining Soda can

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  21. H

    How Does Firing Cannon Balls Affect the Position of a Railroad Car?

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  22. L

    Center of mass for a cylinder with water

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  23. P

    Calculating y-Coord of Center of Mass in Unique Shape

    Homework Statement ____ l _ l l_l l_l Find the y-coordinate of the center of mass. Each side l / _ is length a. I got an answer of 1.25a, but that isn't right. Homework Equations The Attempt at a Solution Area of each section * x-coordinate of center of mass. (the area...
  24. C

    How Far Does the Boat Move When Juliet Joins Romeo at the Rear?

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  25. F

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  26. F

    Find center of mass using rotational equilibrium

    Homework Statement A nonuniform bar is suspended at rest in a horizontal position by two massless cords as shown in Fig. 12-45. One cord makes the angle θ = 15.5° with the vertical; the other makes the angle φ = 58.5° with the vertical. If the length L of the bar is 6.08 m, compute the...
  27. H

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    A thin rectangular plate of uniform areal density σ = 3.13 kg/m2 has length of 44.0 cm and width of 26.0 cm. The lower left hand corner is located at the origin, (x,y)= (0,0) and the length is along the x-axis. There is a circular hole of radius 7.00 cm with center at (x,y) = (16.00,11.00) cm...
  28. D

    How Is the Center of Mass Calculated for a Plate with a Circular Hole?

    Homework Statement A thin rectangular plate of uniform areal density σ = 3.06 kg/m2 has length of 37.0 cm and width of 25.0 cm. The lower left hand corner is located at the origin, (x,y)= (0,0) and the length is along the x-axis. There is a circular hole of radius 6.50 cm with center at...
  29. L

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  30. E

    What happens to the center of mass after a collision?

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  31. B

    Finding Center of Mass - Plate with hole

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  32. C

    Center of mass involving changing positions

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  33. C

    Center of mass of two metal solids.

    Homework Statement Figure 7-29 shows a composite slab with dimensions 22.0 cm multiplied by 13.0 cm multiplied by 2.8 cm. Half of the slab is made of aluminum (density = 2.70 g/cm3) and half of iron (density = 7.85 g/cm3), as shown. How far from the line joining the two metals is the center...
  34. K

    Finding Center of Mass Between Earth and Satellite

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  35. Z

    Solve Easy Center of Mass Homework for Club-Axe

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  36. E

    Center of mass of metal square with a hole

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  37. T

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  38. B

    What is the Center of Mass of a Rod with Varying Linear Density?

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  39. J

    Calculate the center of mass on the force plate

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  40. mg0stisha

    Is There a Center of Mass to the Universe?

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  41. R

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  42. L

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  43. P

    Understanding Center of Mass: Exploring Its Location and Impact on Objects

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  44. T

    Why Is My Calculation of the Center of Mass for a Uniform Wire Incorrect?

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  45. G

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  46. P

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  47. S

    Rotation about the center of mass and spin angular momentum

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  48. T

    Center of Mass: Plate with hole

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  49. K

    Earth & moon rotate round center of mass

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  50. S

    How to Balance a Meter Stick with Unequal Masses at Different Positions?

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