Center Definition and 1000 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. 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...
  2. 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...
  3. 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...
  4. 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...
  5. 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...
  6. tshah321

    Moment of inertia about center of mass with four holes?

    Homework Statement What is the moment of inertia of the 4 kg disk below when it rotates about the center of mass? The mass of the disk without the holes is 6 kg . Homework Equations Center of mass equation: (1/M)(∫xdm) Moment of inertia of a disk: I = 0.5mr2 Parallel axis theorem: I = Io +...
  7. S

    Instant center of Velocity (check if I did it correctly)

    Homework Statement Velocity of point C = 0.2 m/s going down Find VB, VD, Angular velocity of BCD and Angular Velocity of AB Homework Equations V=wr Sine and cosine law The Attempt at a Solution Drawing of the question Please note that BCD is one link (L shape)
  8. T

    I There must be a center of the universe....?

    I am going to state the few assumptions I am making as I ask this question. 1. The big bang was an expansion of space/time rather than a physical explosion, although the general effects seem similar. 2. The universe is not infinite and cannot be if #1 is true. 3. The observable universe is...
  9. M

    Find Area with Theorem of Green - center - radius

    Homework Statement x(t) = 6cos(t)−cos(6t) y(t) = 6sin(t)−sin(6t) 0 <= t <= 2*pi I need to find the area cm2 with Th Green. I need to find the radius and the center coordinate Homework EquationsThe Attempt at a Solution $ = integral 1/2* ( 2*pi$0 ((x)dy - (y)dx) dt ) 1/2 (2*pi$0...
  10. Chrono G. Xay

    Center of Mass of Non-Uniform Rod Using Piecewise-Defined Function?

    How would one go about finding the center of mass of a non-uniform rod when its cross-section has been modeling using a piecewise-defined function? For a specific case let's use a drumstick, noting its volume as a sum of half of a sphere (the 'butt' end), a cylinder (the 'shaft'), the majority...
  11. P

    Book says threonine has chiral center in its sidechain? How?

    Text says that threonine and isoleucine have a chiral carbon in sidechain. I am not seeing it. The carbon in the sidechain that is next to the alpha carbon is attached to an oxygen, a hydrogen, a carbon (a methyl group) and the alpha carbon. So that means its attached to two carbons, so...
  12. I

    Horizontal force on a bicycle dependent on center of mass?

    Hello! If I pedal a bicycle, where is the force that moves the bike forward horizontally applied? Is it the bottom of the back wheel or the center of the back wheel? When the force applied to that point is F, does all that force goes into horizontal acceleration, or does some of that force go...
  13. G

    Bulk velocity and center line velocity

    When using Bernoulli's equation and calculating Reynold's number which one do we use?
  14. A

    Projectile Motion - Center of Mass

    Homework Statement In a fireworks display a rocket is launched from the ground with a speed of 18.0m/s and a direction of 51.0 above the horizontal. During the flight, the rocket explodes into two pieces of equal mass. What horizontal distance from the launch point will the center of mass of...
  15. M

    Bringing cellphone to GRE test center

    I have scheduled a GRE test next week and in the ETS website it says that "Do not bring cell phones, smartphones (e.g., Android®, BlackBerry® or iPhone® devices), PDAs, digital watches, smartwatches and other electronic, recording, listening or photographic devices into the test center". Does it...
  16. hawkeye1029

    Calculating the Center of Mass of a Leg

    Homework Statement Determine the position of the center of mass of a whole leg (a) when stretched out, and (b) when bent at 90°. Assume the person is 1.70 m tall. Homework Equations The Attempt at a Solution This is where I'm stuck...what's the mass? I doubt I can just use variable m because...
  17. phys-student

    Finding electric field at the center of a polarized cylinder

    Homework Statement Consider a uniformly polarized electret in the shape of a cylinder with height h and radius 10h. The polarization in the dielectric is P, parallel to the cylinder axis. a) calculate surface and volume bound charges b) calculate the electric field at the center of the...
  18. Gbl911

    Center of Lift vs. Center of Thrust

    I have been thinking about the CoL and CoT on rockets. I came to the conclusion that they are in the exact same spot on the rocket since your thrust and lift come from the same thing in the same place, the engine. I read some forums on other websites but didn't get a clear answer. It would be...
  19. Titan97

    Electric field at center of charged hemispherical shell

    Homework Statement Find Electric field at center of charged hemispherical shell Homework Equations In spherical coordinates, $$dA=R^2\sin\phi d\phi d\theta$$ The Attempt at a Solution From the image, Enet=2dEy=2dEcosφ $$dE=\frac{kdq}{R^2}E$$ $$dE=\frac{k\sigma dA}{R^2}$$ $$dE=\frac{k\sigma...
  20. Y

    Instantaneous center of velocity for a inverted slider crank

    Homework Statement [/B] Find the instantaneous centers of the linkage below. Homework Equations # of ICs = n(n-1) / 2 The Attempt at a Solution [/B] From the equation above, there are 4(4-1)/2 = 6 ICs in this linkage. But one thing I don't understand is how there are 4 links when 2 and 3...
  21. Ontophobe

    Center of Mass in Elliptical Space

    Apparently, a T-shaped organism in a positively curved space can wiggle around in such a way as to translate itself across space, thereby achieving locomotion simply by changing its shape in a specific series are ways. I've seen a computer generated animation of this and it's actually pretty...
  22. V

    Determining Position and Center of Mass using Reference Frame

    Homework Statement Homework Equations Xcm = (x1m1+x2m2) / (m1+m2) The Attempt at a Solution ok so I'm having trouble understanding what's happening in the question... when the penguin moves, is the sled also moving? If it's friction less ice then if the penguins moves L, the sled will...
  23. Y

    Center of mass in glass of water

    Homework Statement So we have a glass consisting of a 10 cm long cylinder on top of a 1 cm long bottom standing on a table. The radius is 3 cm. For every x in [0, 10] we let h(x) be the height of the center of mass when we fill the glass with x cm water. That is, h(x) is the distance from the...
  24. C

    MHB Find the mass and center of mass of the lamina

    Find the mass and center of mass of the lamina that occupies the region D and has the given density function ρ. D = {(x, y) | 0 ≤ x ≤ 1, −1 ≤ y ≤ 1}; ρ(x, y) = 7xy2 I got my mass to be 7/3 but I'm not sure how to go about finding the center of mass
  25. F

    Is the center of mass fixed in Relativity?

    I think that the center of mass is not fixed in Relativity (unlike in classical physics). Could anyone look at my attached memo and tell me if I am right or wrong.
  26. T

    Velocity of Center of Mass of Disk

    Homework Statement Homework EquationsThe Attempt at a Solution I think if I can locate the instantaneous axis of rotation ,then may be motion/velocity of CM could be determined . In the attached figure I have marked the two points A and B which are instantaneously at rest .The black arrows...
  27. Acemave

    Finding the Center of Mass of a Triangle

    Homework Statement a thin uniform wire is bent to form two equal sides AB and AC of triangle ABC , where AB=AC=5cm . the third side BC , of length 6cm is made from uniform wire of twice the density of the first . the distance of centre of mass from A is ? Homework Equations x centre of mass...
  28. H

    How is the center of mass determined independently of the coordinate system?

    Hi! I have been reading about the position of the center of mass in the Marion's Classical Dynamics book, in some point of the section he states that: "The location of center of mass of a body in uniquely defined, but the position vector R(of the center of mass ofcourse) depends on the...
  29. R

    Center of mass of medicine ball

    Homework Statement 1.68 - ((51(0) + 109(1.5) + 66(3) + 13(0))/(51 + 66 + 109 + 13)) [/B] A person with mass m1 = 51 kg stands at the left end of a uniform beam with mass m2 = 109 kg and a length L = 3 m. Another person with mass m3 = 66 kg stands on the far right end of the beam and holds a...
  30. Destroxia

    How to Determine Priority for a Second Chiral Center?

    Homework Statement The Attempt at a Solution My issue here is the priority, I know OH has the greatest priority, and H the least, but I really cannot figure out the priority of the other 2 bonded to the carbon... ??
  31. Malaxus

    Is it possible for photons to display in the center of room?

    Is it possible for photons to center themselves in mid-air in the center of a room, multiplying and change directions while still being somewhat centered in the room? I have tried looking this up in Google, but all I got were articles which I did not have enough time to read. If this is the...
  32. P

    Force at center of cube due to four charges of equal mag.

    Homework Statement Four charges of 2*10^-7 are placed on the corners of one face of a cube of 15 cm. A charge of -2 * 10^-7 C is placed at the center of the cube. What is the force on the charge at the center of the cube? Homework Equations F = k q_1*q_2/r^2 The Attempt at a Solution...
  33. John Fluharty

    Planet at the center of mass of a binary star system

    I can't think of an instance of this in science fiction, but then I do not have the broadest knowledge of the field, so I could have missed something obvious to everyone else. I wonder, though, could a planet form at the center of mass of a binary star system or be captured there, and could...
  34. J

    Does a Submanifold Correspond to the Center Manifold?

    Hi all, I am not familiar with the dynamic system theory. When I was trying to understand the weakly nonlinear stability analysis, I realize the following question. It is known that the center manifold reduction can be used to study the first linear bifurcation. This lead to the...
  35. J

    Work moving point charge from center of conducting shell

    Homework Statement A point charge q is at the center of an uncharged spherical conducting shell, of inner radius a and outer radius b. How much work would it take to move the point charge out to infinity (through a tiny hole drilled in the shell)? [answer: q2/8πε0)(1/a - 1/b) Homework...
  36. P

    Calculating magnitude of electric field at center of square

    Homework Statement Find the magnitude and direction of net electric field at the center of the square array of charges. Find E_x and E_y The square array of charges http://postimg.org/image/4gf94ymmf/ The Attempt at a Solution [/B] My attempt at drawing in the force vectors...
  37. L

    Exploring Newton's Rings: Why Width of Dark Ring Decreases from Center

    why the width of dark ring decreases as we go away from the center in Newton's rings experiment?
  38. nilesh_pat

    B Find the Center of the Universe?

    Where is the center of Univers or we have still to find the center of universe or there is no center of univers. With regards nilesh
  39. G

    Electric potential at center of charged rod

    Homework Statement Find potential of a uniformly charged rod of length 2a Homework Equations -Superposition The Attempt at a Solution dV=\frac{kλdx}{r}, r=x V=λk\int\limits_{-a}^a \frac{1}{x}\mathrm dx=0 Potential at point B is zero. Is this correct?
  40. A

    Center of mass and Newton's laws of motion

    Homework Statement two particles of 2 kg and 3 kg are at rest . a 6 N force is exerted on the 3 kg particle at t=0. what is the speed of the center of mass at t=5s? Homework Equations F=ma v=u+atThe Attempt at a Solution first i applied f=ma to the 3 kg object and got 2 as the accn. And...
  41. duran9987

    Motion On An Off Center Circle In Polar Coordinates

    Homework Statement A particle moves with constant speed ν around a circle of radius b, with the circle offset from the origin of coordinates by a distance b so that it is tangential to the y axis. Find the particle's velocity vector in polar coordinates. Homework Equations (dots for time...
  42. C

    Does Gravity Cause Heat Flow to the Center of the Earth?

    Here is a review article identifying some causes for the high temperature in the central volume of the Earth. http://www.scientificamerican.com/article/why-is-the-Earth's-core-so/ Inside all massive astronomical bodies like the Earth, collisions of atoms occur in a gravitational field. Because...
  43. U

    Finding the Center of Mass of a Uniform Disc: A Non-Calculus Approach

    Hi New member here! 1. Homework Statement In the figure one-fourth part of a uniform disc of radius R is shown. The distance of the center of mass of this object from center ‘O’ is ………………………. Given: For a semi-circular disc with origin of co- ordinate system at the center of circle, the...
  44. G

    Electric field in the center of uniformly polarized cylinder

    Homework Statement Hollow dielectric cylinder, with inner radius a, outer radius b, and height 2h is uniformly polarized by volume. Polarization vector is normal on the bases of a cylinder. Intensity of polarization vector is given, P. The surrounding area is vacuum. Calculate intensity of...
  45. E

    Moving center of mass, torque and axis of rotation

    Hello. Suppose I have a coordinate system with the origin at the center of mass at rest of some rigid object and I wish to calculate the total change in angular momentum of the object with respect to it's center of mass. If I apply a torque to the object, that also happens to be an unbalanced...
  46. N

    Center of Mass of open top cylinder

    Homework Statement The attached diagram shows a uniform density hollow cylindrical shell with a solid bottom and an open top. It has radius R and height h. Find the height for the center of mass of this cylinder, taking the origin of the coordinate system at the center of the bottom. Use "pi"...
  47. P

    Center of a irregular hexahedra given the vertices

    I am trying to compute the center of irregular convex hexahedras (6 faced volume). I have the 8 indices that define the hexahedra. I was reading that the center is simply the sum of the indices divided by the number of indices and this is true for all polygons and polyhedras. Is this true?
  48. J-dizzal

    Center of mass project exploding at max height

    Homework Statement A shell is shot with an initial velocity http://edugen.wileyplus.com/edugen/shared/assignment/test/session.quest2529559entrance1_N10030.mml?size=14&ver=1436312588112 of 17 m/s, at an angle of θ0 = 63° with the horizontal. At the top of the trajectory, the shell explodes into...
  49. J-dizzal

    Center of mass of two connected different density blocks

    Homework Statement The figure shows a composite slab with dimensions d1 = 11.6 cm, d2 = 2.85 cm, and d3 = 13.4 cm. Half the slab consists of aluminum (density = 2.70 g/cm3) and half consists of iron (density = 7.85 g/cm3). What are (a) the x coordinate, (b) the y coordinate, and(c) the z...
  50. KylieVegas

    B What is the center of the universe?

    I read in a book that there is no center of the universe because for example, you put dots around a balloon, and when you put air into the ballon, the dots will separate from each other, and each dot will see themselves as the center of the balloon, depending on the dots' perspective. That only...
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