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.

View More On Wikipedia.org
Recent contents Top users
  1. Daleri Mc Rileda

    B How Far Is It To The Center Of The Milky Way/Tootsie Pop?

    With length contraction being ever increased while approaching the mass of a black hole singularity, how does one measure the distance to the virtual infinite contracting frames of reference of time and space /distance of the singularity? Related question : How can one measure the size of a...
  2. N

    Instantaneous Center: How to Solve Homework Equations

    Homework Statement Determine the angular velocity of the gear at the instant shown. Set v = 9ft/s and vc = 6ft/s. Assume counterclockwise is positive. Homework Equations v = w x rIC The Attempt at a Solution I tried solving this many times using va = v0 + (ω x ra0 ) and vb=v0 + (ω x rb0 )...
  3. R

    Finding Mass Center of a Circular Disc with Hole & Weight

    Why do we take the Center of mass to be on the right side rather than on the left? A uniform circular disc of radius 4a with a circular hole of radius 2a made in the disc. The mass of L is m and a particle of mass km is now fixed to L at the point P. The system is now suspended from the point S...
  4. T

    Curvature of electric field around center of a quadrupole

    Hello all. I am working on a research project involving the Stark effect and its application in molecular guides and came across a bit of math in a paper that I don't understand. In this paper http://arxiv.org/abs/physics/0310046 there is an equation in the introduction concerning the electric...
  5. B

    B Does time stop at the center of a black hole?

    If time does indeed come to a stop at the event horizon, how are we even able to observe it? Wouldn't it cease to exist to someone moving through time the moment time comes to a halt on the event horizon?
  6. E

    Center of gravity change and acceleration

    Hello Community My first post here so excuse me in case i posted in the wrong place. I basically have to write a paper in school about a physics topic. This includes creating graphs with independent and dependant variables and finding the slope. It should be something to complicated but also...
  7. S

    B Using center of mass for loop de loop

    A quick question, I remember my professor said to use the center of mass for solving the classic loop de loop problem. For example, he wanted us to use the distance from the surface of the loop to the center of the object (instead of just from the loop to the surface of the block) for the height...
  8. T

    B Rod falling radially towards the center of a mass

    This example might be not very interesting, but perhaps helps to improve my understanding. Is a radially falling rod in free fall? Which frequency shift of light emitted at the ends of the rod would observers at rest at the respective other ends measure? Here are some assumptions. Please...
  9. Zarich12

    B How to find the center of gravity of an object

    Is there a relatively simple way to find the center of gravity of an object? I need to know to see if my model rocket has a high center of gravity. The bulk of he weight is in the bottom.
  10. ing_it

    Physical Pendulum - Rod - Period and Distance From Center of Mass

    Homework Statement We have a rod (length L, mass m) suspended at a point whose distance from the center of mass is a. 1) prove that (generally) there exist two values of a (a1, a2) for which the pendulum oscillates with the same period. 2) derive and explain: T = 2\pi\sqrt{\frac{a_1+ a_2}{g}}...
  11. G

    B What kind of force acts in the center of the Earth?

    What kind of force acts in the centre of the Earth ? What is the intensity ?
  12. RJLiberator

    Understanding the Center and Centralizer of a Dihedral Group

    Homework Statement If n ≥ 3, show that Z(D_n) = C(x) ∩ C(y). Homework Equations G is a group, g∈G C(g) = {h∈G: hg = gh } The Centralizer of g Z(G) = {h∈G: hg = gh for all g∈G} The center of G ∩ means the set of all points that fall in C(x) and C(y). Every element of D_n can be uniquely...
  13. S

    Magnitude of the E-Field at the center of curvature

    Homework Statement A circular rod has a radius of curvature R = 8.11 cm, and a uniformly distributed positive charge Q = 6.25 pC and subtends an angle theta = 2.40 rad. What is the magnitude of the electric field that Q produces at the center of curvature? Homework Equations E = kQ/r^2 6.25 pC...
  14. Allen_Wolf

    B Gravity in the center of the Earth (a confusion)

    I have learned that the gravity at the center of the Earth is zero. I guess its because it gets balanced as the force from all the sides are equal in magnitude and opp in direction. But several land forms throughout the world having different masses could cause a distortion which could make an...
  15. Josephthe2

    Calculating deflection with rotation about center support

    I am preparing for a qualifying exam for my PhD program and am looking at some of the old tests from previous years (as supplied by the school for study/prep material). I have come across a deflection problem that has me stumped, and I might just be overthinking it. The problem:
  16. P

    Calculating Center of Mass in Cylindrical Coordinates

    Homework Statement Determine the center of mass in cylindrical coordinates of a cone with constant density ##\rho(\vec{r})##. (The cone is inverted, i.e. it's thinnest point is at ##z=0##.) Homework Equations ##m=\int\int\int_C \rho r \, drdzd\theta## ##\overline{r}=\int\int\int_C r\cdot r\...
  17. Monoxdifly

    MHB [ASK] Distance from the Upper Base to the Center of Dodecahedron

    I want to prove the formula of regular dodecahedron's volume. For this, I need to split the dodecahedron to 12 pentagonal pyramid with the same size. However, I don't know how to determine the height of those pentagonal pyramids. Any references I had encountered involving either golden ratio or...
  18. X

    B Gravitation with multiple objects by using center of mass

    Four 9.5 kg spheres are located at the corners of a square of side .60 m. Calculate the magnitude and direction of the total gravitational force exerted on one sphere by the other three. So, essentially my question is, why can I not use center of mass of the other 3 spheres to calculate the...
  19. Elvis 123456789

    Magnetic Field at the center of a square loop

    Homework Statement A square wire loop 12.0 cm on each side carries a clockwise current of 15.0 A Find the magnitude of the magnetic field at its center due to the four 1.30 −mm wire segments at the midpoint of each side. Homework Equations B = (μ0*I)/(4π)*(2a)/(x√(x^2+a^2)) The Attempt at a...
  20. Alltimegreat1

    Direction of stars' orbits around galactic center

    Do all stars in the Milky Way orbit the galactic center in approximately the same direction? Also, toward which Zodiac constellation is the Sun moving in its orbit?
  21. Elvis 123456789

    Magnetic Field at center of a Square loop

    Homework Statement A square wire loop 12.0 cm on each side carries a clockwise current of 15.0 A Find the magnitude of the magnetic field at its center due to the four 1.30 −mm wire segments at the midpoint of each side. Homework Equations B = (μ0*I)/(4π)*(2a)/(x√(x^2+a^2)) The Attempt at a...
  22. F

    Center of Pressure: 2b/3 from Free Surface

    Homework Statement can someone explain about the Fr acting at a distance 2b/3 from free surface firectly beneath the centroid of the surface ? Homework EquationsThe Attempt at a Solution does the author mean the center if pressure ( point where the FR acts) of the completely submerged plate...
  23. F

    Finding the center of mass in a system of pipes

    Homework Statement System S is static and is comprised of 3 identical metal pipes A, B and C which are placed so that A lays ontop of B and C. B lays into the y axis. The length of the pipes are orientated parallel with the z axis. The outer and inner radius of each pipe is (Outer : 0.51m)...
  24. F

    Center of Buoyancy: Finding the Answer

    Homework Statement the buoyancy force i found id 0.751(1000)(9.81)(0.5x0.55x0.96) = 1945N , i also found that the center of gravity of submerged portion is (48/3 , 55/ 30 = (16 , 18.3) , how to find the center of buoyancy ? is the cnter of buoyancy acted half of the submerged portion , which is...
  25. A

    A Project img on X-Y surface to a cylinder placed in center....

    Hi , I came across a problem ,I've search a lot but couldn't exactly find the solution. here is my problem: suppose there is an image ( I call it IMG_A),place IMG_A in the X-Y plane , put a mirror cylinder at the center of IMG_A. what we see in the cylinder mirror is a deform image (I call it...
  26. U

    Determine the location of her center of mass

    Homework Statement To determine the location of her center of mass, a physics student lies on a plank of weight 100.0 N and length 2.5 m supported by two scales 2.50 m apart. The left scale reads 420.0 N, and the right scale reads 210.0 N. (Note: Don’t neglect the weight of the plank when you...
  27. W

    Center of gravity vs center of buoyancy

    Homework Statement why the floating body still stable when G ( center of gravity ) is above the B ( center of buoyancy)? Homework EquationsThe Attempt at a Solution in my opinion , the statement is worng , because when G is above B , G has the tendency to move downward , causing the object to...
  28. P

    Is the center of mass truly where all forces act in a system?

    As far as I know in a system of particles or a body there is a point that behaves like all the forces on the system are applied at this point, but are these forces really applied in this point? Can you explain please, I thought at this and I arrived at the conclusion that these forces aren't...
  29. T

    B The Center of the Earth and Black holes and Gravity

    a related thought experiment to a tunnel through Earth through which a person falls to the other side, is what if it was a pendulum falling through the planet? first, a pendulum is at 90 degs to the G field; 2nd, as soon as the pendulum BEGINS to fall through, it is in free fall, and it will...
  30. S

    MATLAB Center Wavelength of Fiber Bragg Grating Filter

    I would like to locate the center wavelength of a FBG notch filter in MATLAB, but I'm having trouble getting an answer within 0.01nm of the correct wavelength. So far I've tried using a quadratic fit with MATLAB, but that is too dependent on the amount of data points to the left and right of...
  31. H

    Automotive How do Center differentials work

    Greetings all, In my quest to imagine the ultimate sportscar, I began to wonder about the following: Certain cars are All Wheel Driven (AWD) and they do so via a Center differential delivering power to both axles. Amongst those cars, some have fixed Torque Bias/Split Ratio, which doesn't alter...
  32. 4

    Center of mass and momentum in boat question

    Homework Statement A person with mass m is sitting on one end of a lifeboat of uniform density. Mass of lifeboat is 3m. The person then walks a distance of L to the other side of the lifeboat. Which of the following statements best characterizes the motion of the lifeboat? " The lifeboat...
  33. evinda

    MHB Finding the Center of $S_n$: Understanding the Commutativity of Disjoint Cycles

    Hello! (Wave) I want to find the center of $S_n$. $Z(S_n)=\{ c \in S_n: cg=gc , \forall g \in S_n\}$.Every $c\in S_n$ can be written as a product of transpositions, $$c = \prod_{i = 1}^r (1\, m_i)$$ for some $r$ and some sequence $(m_i)_{1\leqslant i \leqslant r}$, right? Doesn't this imply...
  34. S

    Can a Center Tapped LC Circuit Reduce Potential Difference Across the Inductor?

    My objective is to make a lc circuit that will have a potential difference across the inductor that is lower than that of the capacitor. A spark gap must also be used. Will this work and will the resonant frequency be the same as if it was wired conventionally?
  35. evinda

    MHB Finding the Center of $GL_n(\mathbb{R})$: Exploring the Possibilities

    Hello! (Wave) I want to find the center of $GL_n(\mathbb{R})$. $Z(GL_n(\mathbb{R}))=\{ c \in GL_n(\mathbb{R}): cg=gc \forall g \in GL_n(\mathbb{R}) \}$ I have thought the following. Let $c \in GL_n(\mathbb{R})$. Then there is a $b \in GL_n(\mathbb{R})$ such that $cb=I$ where $I$ is the $n...
  36. websterling

    LIGO GW150914 Data Release & Tutorial

    https://losc.ligo.org/events/GW150914/']The[/PLAIN] LIGO Open Science Center has released data from the gravitational wave detection along with a tutorial going through some typical signal processing tasks on strain time-series data associated with it. GW150914 Data Release From the tutorial...
  37. CrackerMcGinger

    B How exactly do SMBHs in the center of galaxies form

    I've been thinking for awhile now, and I still don't understand how these types of black holes form, since they can't form by conventional means.
  38. SDewan

    How Does External Force Affect a Rotating Disc and Ring System?

    Homework Statement A heavy ring of mass m is clamped on the periphery of a light circular disc. A small particle of equal mass is placed at the center of the disc. The system is rotated in such a way that the center moves in a circle of radius r and with a uniform speed v. Find the external...
  39. gracy

    Velocity of charge at the center thrown from far away point

    here from time 0:53 to 0:58 velocity at center would be more than or approximately equal to zero .I want to ask why approximately zero why not zero?
  40. CrazyNinja

    Atom Nucleus: Geiger/Marsden Experiments & Results

    How do we know that the nucleus is at the center of the atom? I know about the Geiger/Marsden experiment and also of its results. They observed a few α-particles scattering almost at 180°. Hence they concluded that there must exist a high density, positively charged "center" in the atom. But on...
  41. L

    Center of Mass of separating Orbiting Mass

    I was reading about the ISS earlier, and this question came into my mind, and I can't seem to decided how this actually works. Here's the set-up: Say I have two masses stuck together (m1 and m2) to form a mass M in orbit around some planet (like the ISS, and some large space capsule that is...
  42. G

    Transforming Equations: How to Solve for 3-22a | Center of Pressure Homework

    Homework Statement pls refer to photo 2 , (circled part) How to transform equation in 3-20 to become equation in 3-22a ?Homework EquationsThe Attempt at a Solution i have tried in photo 3 , yet can get the same form as in 3-22a . In step 2 , i divided the y_p with Fr
  43. T

    MHB Starting with center of thrust to find amount of force on each point?

    I'm playing a game, From the Depths, that let's you build your own helicopter blades (and put them on ships that you build) and program in LUA. I did some searching and found: Calculating the Center of Thrust on Multirotors | Flite Test Currently, there is no way to tell how much lift a given...
  44. E

    Integrals to Solve Area and Center of Mass of a Cut Circle

    Homework Statement I am after finding the centroid of the remaining area (hatched) when a circle is cut by a line. I made a diagram in CAD that demonstrates the problem. The idea is that, starting from the bottom of the circle, a cut is taken leaving a remaining shape whose area and...
  45. A

    B How to calculate center of mass & centerline a of a boat?

    Can anyone explain how to calculate the center of mass of a boat? and the centerline of a boat? Formulas, websites, anything helpful, just to let you know I haven't taken any high level physics classes so i don't know any of the fancy stuff lol. Thanks for the help
  46. W

    Glancing elastic collision, and center of mass

    Homework Statement So this is just something i came up with to check if i am understanding everything allright, it all comes down to collisions in regard to the center of mass So two "masses" experience a glancing collision M1: vi - 3m/s (refered to as v1i) ; m - 2Kg (m1) M2...
  47. S

    Rolling Bottle: Calculating Acceleration of Center of Mass

    Homework Statement There is an empty bottle described as an hollow cylinder, that lies on a paper. Now the paper is pulled with an acceleration a, so that the bottle starts rolling perfectly on the paper. (Have a look at the figure.) Homework Equations Calculate the acceleration of the center...
  48. L

    Optics: Center of Fizeau Fringe? Michelson Interferometer

    Hello everyone, i am simulating a Michelson interferometer, where one mirror is slightly tilted, see picture.. This results in circular arcs / hyperbolic cross-section fringes. The center of these fringes depends on the focal length i am using, see picture. Is there an analytical expression for...
  49. A

    Current through Earth's center to produce magnetic field

    1. The field strength of the Earth is 5x10^-5 T at the surface. Space shuttles orbit the Earth at a speed of 7860 m/s . They orbit at an altitude of 322 km. If we assume that a single current loop at the Earth's radius is generating the magnetic field, then what is the current? Determine the...
  50. P

    Calculating Charge at the Center of a Spherical Shell has me stumped

    Edit: Forgot to type "stumped" at the end of the title 1. Homework Statement Instead of typing it out, a link to a scanned document of the problem is here: http://imgur.com/Be3jSLp. Homework Equations The equations to use are stated in the problem here: http://imgur.com/Be3jSLp The Attempt...
Back
Top