Centre of mass Definition and 219 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

    Understanding Centre of Mass Motion: E + $\sum_{i < j}(F_j_i + F_j_j)$

    I was looking over my notes for centre of mass for a system and it says: c = \frac {1} {M} \sum_{i} m_i\ddot{r}_i = \sum_{i}(E_i + \sum_{j \neq i}F_i_j) where M is the total mass of the system. Then it considers the centre of Mass in motion: M \ddot{c} = \sum_i m_i \ddot{r}_i =...
  2. S

    Calculate Centre of Mass with Unknown Mass: Ricardo & Carmelita on Canoe

    Ricardoof mass 80Kg, and Carmelita, who is lighter, are enjoying Lake Merced at dusk in a 30Kg canoe. When the canoe is at rest in the placid water, they exchange seats, which are 3m apart and symmetrically located with respect to the canoe's centre. Ricardo notices that the canoe moves 40 cm...
  3. S

    How Far Does the 40Kg Skater Move?

    Hi, I must be doing something wrong...because i found this question wayyyy too easy. Two skaters, one with mass 65Kg and the other with mass 40Kg stand on the ice rink holding a pole 10 m long and a negligible mass. Starting from the ends of the pole, they pull themselves along the pole...
  4. S

    Finding the Centre of Mass of a Cubical Container

    A cubical container has been constructed from metal plate of uniform density and negligible thickness. The box has an edge length of 40 cm. Find the x, y, & z coordinates of the centre of mass of the box. Im guessing that the x and y coordinates are found by the symmetry..But how do i...
  5. P

    Conservation of Energy, Centre of Mass and Linear Momentum

    Well here are 5 questions from my text which I've tried doing but can't seem to twist my ahead around to figure them out. I don't know if it's due to the fact that I'm not applying the relevant concepts. Thanks for any help. (1). A uniform cord of length 25cm and mass 15g is initally stuck to...
  6. B

    Finding Centre of Mass for a Uniform Semicircular Lamina

    Where is the centre of mass of a semicircular lamina which is uniform? I know it is somewhere along the line of symestry, but where excactly?:confused:
  7. T

    Question of centre of mass and parallel axis theorem

    A puck of mass 80.0 g and radius 4.20 cm slides along an air table at a speed of 1.50 m/s. It makes a glancing collision with a second puck of radius 6.00 cm and mass 140.0 g (initially at rest) such that their rims just touch. Because their rims are coated with instant-acting glue, the pucks...
  8. C

    Understanding Centre of Mass in Physics

    why is the concept centre of mass?
  9. R

    The Death of the Centre of Mass Theorem.

    Many people believe that the Centre of Mass Theorem is a powerful and useful tool in Newtonian Mechanics. In fact it is a farce. (1) It is trivially true at distances in which the massive object is virtually a point-mass, such as between distant stars. (2) It is completely incoherent and...
  10. G

    Internal forces and centre of mass

    heres another conceptual one . there is a standard yet very elegant problem about a rocket bllowing up mid air and finding the final postions of the parts of the projectile using the principle of centre of mass remaining the same since the forces a re internal when the rocket blows up . now...
  11. W

    Calculating Centre of Mass for Connected Masses: Exploring Ratios and Distances

    Hello I was given a question of 2 masses m_a and m_b whos centres of L distance apart and are connected by a massless rod (so it kind of looks like a dumb-bell). Each ball through its centre has an axis perpendicular to the rod (axiz a and b respectively) and each has a moment of inertia...
  12. O

    Centre of Mass of a Truncated Sphere

    Alright... I've been struggling with this derivation for QUITE some time, and I can't get a hold of my TA... so... I'm trying to derive the centre of mass of a truncated sphere. The final answer is cm= -(3h^2*(R-h/2)^2)/(4R^3-3Rh^2+h^3) Where R is the radius of the full sphere, and h is the...
  13. T

    What Is the Possibility of Higher Dimensions in the Universe?

    What we humans know about the center of mass of Universe?
  14. D

    Calculating the Centre of Mass in a 2-Body System

    A little question: as a planet (such as jupiter) orbits the sun, both the planet, and the sun orbit the same point of the centre of mass. how do you calculate where that centre of mass is? (2 body problem only) thanks DH
  15. R

    Integration of a cone to find centre of mass

    Can anyone help me with this question? A uniform solid cone of height b and base radius a stands on a horizontal table. Find an expression for the volume of the disc at height h above the base. Integrate over all the discs to show that the total volume, V, is given by V =pi/3 * b * a^2
  16. S

    Measuring g, but not knowing the centre of mass - problem?

    Hiya! I'm confused, for my Physics A2 Coursework we're measuring g (gravitational field strength) and I don't know the centre of mass of the pendulum. Will this affect my experiment and/or results? Should I do something to overcome it? Please Help! Sam(antha) xx
  17. S

    Complicated Centre of Mass Question

    :cry: Hey all... I'm having trouble deciding where the heck I should even start with this question. Soooo... here it is (I've attached a picture of the diagram because the question wouldn't make any sense without it). A non-uniform bar of weight W is suspended at rest in a horizontal...
  18. N

    Centre of Mass & SHM: Help Understanding & Graphing

    Hi, I have a hard time trying to understand the Centre of Mass as well as the graphing for SHM. Please help. Thanks heaps.
  19. S

    Is Belief Necessary for Scientific Discovery?

    Hi guys, I am exploring the notion that at the centre of all mass or intensities is a centre of absolute nothing. I won't go into why I am exploring this but the question that is of interests is : How can "nothing " be proved either in theory or by evidence except by default? And If...
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