What is Center of mass: Definition and 914 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. D

    Center of gravity (it's not center of mass )

    Center of gravity (it's not center of mass!) Hi, I'm a very desperate person right now. For two days (I'm totally dumb) I've been trying to calculate the center of gravity of two rigid bodys... Look, it's not the center of mass (I'm not that dumb!). OK, here's the problem...(at least one of...
  2. M

    Calculating Center of Mass of a Hollow Nose Cone

    I am working on a rocket and need to find the center of mass of a hollow nose cone. Any help would be appreciated.
  3. P

    Calculating Center of Mass for a System of Spherical Masses on the x-axis

    Hi, here is the problem: Imagine three spherical masses all fixed on the x-axis: mass 5M at the origin, mass 2M at x =+12.0 units, and mass M at x = -8.0 units, all connected by a rigid rod whose mass can be ignored. At what position along the x-axis is the center of mass of the system...
  4. PeteGt

    Center of mass and REduced mass

    I forget how these two relate both conceptually and mathematically...any help?
  5. S

    Inertia and Center of Mass?

    Inertia and Center of Mass?? I'm a bit confused about finding the moments of Inertia for objects, I know I=Icm+MD^2 but what exactly is D, is it the distance from the Center of Mass to the pivot point, can someone please explain this to me? :confused:
  6. S

    Solving Center of Mass Prob: Stick Length 0.25m, Mass 0.53kg

    Can someone please help me with this problem, a hint, anything something? A girl throws a stick with a length of 0:25 m and a mass of 0.53 kg into the air in such a way that the center of mass rises vertically. At the moment it leaves her hand, the stick is horizontal and the speed of the...
  7. J

    Find Initial Acceleration of Rod's Center of Mass with Newton's 2nd Law

    here's the question: A uniform rod of length 1.15 m is attached to a frictionless pivot at one end. It is released from rest from an angle of 27 degrees above the horizontal. Find the magnitude of the initial acceleration of the rod's center of mass. So far I've only been able to figure...
  8. J

    Is this a center of mass question?

    Question: Find the solid angle subtended at the origin by a thin circular disk of radius a, whose cente is a distance b from the origin and where the normal to the disk is parallel. Do I have to find the center of mass to solve this question?
  9. D

    The center of Mass perfectly match the center of Force->

    In a system of several masses the center of force has same position with the center of mass in the geometrical space; Yes or No? Please explain why!
  10. D

    Understanding Center of Mass: Exploring the Concept of Vector Mass and Position

    This is attempt to address Arcon's page on center of mass He says: \vec{R}=\frac{\sum m_i\vec{r_i}}{M} R is radius vector of the center; ri are radius vectors of mi; M is sum of all mi; It can be generalized to vector mass too...
  11. S

    Finding the Center of Mass of a Uniform Semicircular Disk Using Integration

    Show that the center of mass of a uniform semicircular disk of radius R is at a point (4/(3*Pi))R from the center of the circle. well I know I am suppose to find this by integration. By this equation M\vec{r_{cm}}=\int\vec{rdm} But, I am not sure how to find dm in this case... do I...
  12. P

    Calculating Center of Mass for a Circular Hole in a Uniform Square Sheet Metal

    A circular hole of diameter 11.1 cm is cut out of a uniform square of sheet metal having sides 22.2 cm, as in the figure. What is the distance between the center of mass and the center of the sqaure? i need some serious help with cm, i don't get this at all.
  13. P

    Center of mass particle problem

    A 4.01g particle is moving at 1.36 m/s toward a stationary 9.43g particle. With what speed does the heavier particle approach the center of mass of the two partciles? i don't get how cm relates to finding speed The mass of a star like our sun is 347000 Earth masses, and the mean distance...
  14. C

    Finding the Center of Mass in a Divided Square

    Imagine a square with side length "a". Now, divide the square into 4 equal squares with side length "a/2". In the top righthand corner of the large square, a circle with radius "a/4" is cut out, which also removes the top corner piece. What is the new center of mass? (The origin is at the center...
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