What is Center: Definition and 1000 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. S

    Electrical Load center terminal screws - where to buy?

    Where can a person buy the small screws that hold the wires into terminals in a SquareD brand load center (breaker box) ? Places sell the screws that hold the panel cover on a a breaker box. They also sell the "lugs" that hold very large wires. However, what I'd like is a package of the...
  2. Indula

    How to calculate the inductance of a center tapped solenoid ?

    I'm trying to drive a transformer using a ZVS power supply. The primary coil that we use here has to be wound center tapped. The output frequency depends on the inductance of the primary winding and capacitance used in the circuit. The circuit of a ZVS power supply is as follows, The...
  3. LordWhiplash

    I Why is the lowest energy level close to the center?

    While studying photon emission, I noticed that I never really understood why the higher energy level is farther from the center of the atom. To me it seems counterintuitive, because usually the forces of attraction are greater at shorter distances, which would imply a higher energy consumption...
  4. F

    Inverted pendulum -- What force is applied at the center of mass?

    Summary: I know that in order to keep inverted pendulum balanced when it leans forward, I should accelerate the bottom of it, but what is the force which is applied to center of mass of the pendulum with balances torque due to gravity? Is it inertial force? We assume that our inverted pendulum...
  5. lLehner95

    Find the photon energy in the center of mass frame and vice versa

    I tried to use the Lorentz transformation: ##E^{*}_{\gamma }=\gamma _{cm}E_{\gamma }-\beta _{cm}\gamma _{cm}p_{\gamma }## We have a photon, so it becomes: ##E^{*}_{\gamma }=\gamma _{cm}E_{\gamma }(\beta _{cm}-1)## Unfortunately, the solutions say that the correct way is to use the inverse...
  6. B

    I Calculating Bin Center for Rate vs Energy Plot

    Hello! I want to plot a rate vs energy plot, but I am not sure how assign the bin center. Assume I have 2 data points in the bin (so 2 energy values), ##E_1## and ##E_2## and the first one has 100 counts measured over 10 seconds (so a rate of 10 counts/s) while the second one has 2000 counts...
  7. Nimarjeet Bajwa

    How can we find the center of mass of a solid cone?

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  8. Jelsborg

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  9. A

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  10. Euge

    MHB What Is the Center of the Ring of All \( n \times n \) Complex Matrices?

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  11. JD_PM

    I Two rings rotating about a common center

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  12. jisbon

    Help Me Solve My Diagram Problem: Calculating Center of Mass

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  13. Like Tony Stark

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  14. Seth Greenberg

    What is the angular velocity in the center of a rotating disc?

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  15. paulmdrdo

    Engineering Finding the center frequency and bandwidth of a Pass-band filter

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  16. Prabs3257

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  17. jordy1380

    Intro Physics Principles of Technology by the Center for Occupational Research and Development

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  18. E

    Calculating the Center of Mass

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  19. F

    Reflection and Rotation Centers in D_n: Finding C(F) and C(R) for Even and Odd n

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  20. brotherbobby

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  21. e2m2a

    Center of mass momentum of a photon and electron system

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  22. Benjamin_harsh

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  23. S

    Fixed-End Beam with Center Static Load

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  24. arcTomato

    How can we determine the distance to the Galactic center?

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  25. S

    Classical Book about center of mass frame of reference and fictitious force

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  26. R

    Center of Mass of acceleration and velocity

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  27. P

    What are the steps for calculating the center of mass of this object?

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  28. S

    Center surround detection explained?

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  29. R

    What is the solution to the Center of Mass problem?

    I was able to find the y and z axis. To find the x-axis I was assuming they would be the same for both of the slab parts and since the center of mass is the middle of the cube it should be halfway between 14.0 cm, which is 7.0cm. I can't think of any other reason why it would not be.
  30. C

    MHB How can we prove that the center of a ring is a subring?

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  31. Lone Wolf

    Finding the center of mass of a homogeneous object

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  32. RicardoMP

    How to determine particle energies in center of momentum frame?

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  33. P

    I Center of Mass of a jetpack-Earth System

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  34. D

    How to find the center of mass of a cube?

    Homework Statement Find the center of mass of a homogeneous solid cube with side ##L## analytically. Homework Equations None. The Attempt at a Solution I don't understand how to find the center of mass on three dimensions. I know that since it is homogeneous, if I center the cube on the...
  35. D

    Find the center of mass of a plate

    Homework Statement Find the center of mass of the next plate if: A) Is homogeneous B) Its density per unit mass is ##\sigma=Axy##, where ##A## is a constant. Homework Equations ##X_{cm}=\frac{\int\sigma x dA}{\int\sigma dA}## ##Y_{cm}=\frac{\int\sigma y dA}{\int\sigma dA}## The Attempt at a...
  36. J

    Finding the POSITION of the center of mass

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  37. H

    Effect of the Location of the Center of Mass on the Falling Time....

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  38. E

    Where is my mistake? (Pure rolling and center of mass)

    Homework Statement A cylinder with a mass of M and radius R is attached to a spring with a constant of k. The attachment always stays the same as described in the picture. The cylinder is moved to the right and the released, and it rolls without slipping (pure rolling). What will be the...
  39. Zack K

    Potential at center of sphere of radius R and charge -Q

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  40. Athi Sankar

    Why does radial acceleration act toward the center?

    Acceleration of a rotating link has two components,Tangential (change in the direction) Radial (change in the magnitude). Why the direction of Radial acceleration is considered towards center (Centripetal)? what about centrifugal?
  41. K

    Problem when calculating the center of mass of a triangle

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  42. Hiero

    Torque about center of mass due to Coriolis force, is it 0?

    It’s essentially a question about cross product identities. I want to analyze a problem in a frame of reference which is rotating with angular velocity ##\vec \Omega## relative to an inertial frame. In this non-inertial frame, we have a rigid body rotating with constant angular velocity ##\vec...
  43. D

    Equilibrium : normal reaction of a rotational center?

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  44. E

    Angular momentum conservation and center of mass

    Homework Statement Two bodies with an equal mass of M are attached by a pole with no mass with a length of L. The system is placed on a horizontal table and at first it is at rest. At t=0 a bullet with a mass of m hits the pole, as described in the picture. The collision is completely elastic...
  45. F

    Body rotating about its center of mass

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  46. artworkmonkey

    Calculate the density at the centre of the Sun

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  47. gimak

    Programs Working at the center for Computational Quantum Chemistry

    Hello, I'd like to work in the above named center at the University of Georgia in Athens, Georgia under Dr. Henry Schafer. However, he's a professor in the chemistry department. I'm guessing if I go in the university as a physics graduate student I can't have him as a Ph.D advisor. However, is...
  48. RandyD123

    B Big Bang Theory: If There's No Center, How Is Universe Infinite?

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  49. M

    B Moving Center of Mass Collisions

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  50. A

    Commutator group in the center of a group

    Homework Statement [G,G] is the commutator group. Let ##H\triangleleft G## such that ##H\cap [G,G]## = {e}. Show that ##H \subseteq Z(G)##. Homework EquationsThe Attempt at a Solution In the previous problem I showed that ##G## is abelian iif ##[G,G] = {e}##. I also showed that...
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