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Center of Mass: Introduction

Center of Mass: Introduction

Any object that obeys Newton's second law of motion is made up of a large number of infinitesimally small particles. Objects in motion can be as simple as atoms or as complex as gymnasts performing in the Olympics. The motion of such objects is described about a point called the center of mass of the object. The center of mass of an object is a point that acts as if the whole mass is concentrated at that point. The center of mass of an object with a large number of infinitesimally small...

Moments and Centers of Mass

Moments and Centers of Mass

A flat metal plate, or lamina, balances at a point called its center of mass. This point depends not only on the shape of the plate but also on how mass is distributed throughout it. If the material has variable density, some regions contribute more to the balance point than others. Mathematically, the center of mass is treated as a weighted average of all points in the plate, where the weights are determined by density.Suppose the plate occupies a region D in the xy-plane, and its density at...

Center of Mass

Center of Mass

The center of mass is the point at which the total mass of an object can be said to be concentrated. It is a fundamental principle in mechanics and physics that applies to all objects regardless of their shape or size. The center of gravity is the point at which an object’s weight appears to be concentrated and can be used to balance the object perfectly.
The knowledge of the center of mass can also help us to describe and predict the motion of objects. For example, when a ball is thrown into...

Applications of Integration to Find Centers of Mass

Applications of Integration to Find Centers of Mass

Rotational equilibrium provides a natural framework for defining the center of mass of a system. For a plank balanced on a pivot with two unequal masses, equilibrium is achieved when the net torque about the pivot is zero. Torque is defined as the product of a force and its perpendicular distance from the pivot. When the torques due to all forces cancel, the pivot coincides with the center of mass of the system.For a system composed of several discrete point masses, the center of mass lies at...

Equation of Motion: Center of Mass

Equation of Motion: Center of Mass

The equation of motion for a single particle can be expanded to encompass a system of particles consisting of n particles. For any arbitrarily chosen particle within this system, the net force acting upon it is the aggregate of both internal and external forces. Extending this principle to all particles within the system results in the equation of motion for the entire assembly.
Internal forces between any pair of particles manifest as collinear pairs of equal magnitude but opposite directions,...

Significance of Center of Mass

Significance of Center of Mass

The center of mass of an object is defined as the mass-weighted average position of all the particles that comprise the object. The significance of the center of mass of an object can be seen by looking at its dynamics. The time derivative of the center of mass gives its velocity, assuming that the object's mass remains constant over time. Furthermore, the total linear momentum of an object can be seen as the linear momentum of a single particle of the object's total mass moving with the...

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Related Experiment Video

Updated: Jul 17, 2026

Oscillation and Reaction Board Techniques for Estimating Inertial Properties of a Below-knee Prosthesis

Oscillation and Reaction Board Techniques for Estimating Inertial Properties of a Below-knee Prosthesis

Published on: May 8, 2014

Center of mass function approximation.

A L Betker¹, Z Moussavi, T Szturm

¹Dept. of Electr. Eng., Manitoba Univ., Canada. abetker@ieee.org

Conference Proceedings : ... Annual International Conference of the IEEE Engineering in Medicine and Biology Society. IEEE Engineering in Medicine and Biology Society. Annual Conference

|February 3, 2007

Summary

This study introduces a hybrid genetic algorithm sum-of-sines model to estimate the center of body mass (COM) trajectory using accelerometers. This accessible method offers promising clinical applications for assessing balance and postural control.

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Last Updated: Jul 17, 2026

Oscillation and Reaction Board Techniques for Estimating Inertial Properties of a Below-knee Prosthesis

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Published on: May 8, 2014

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Published on: November 15, 2013

Area of Science:

Biomechanics
Human Postural Control
Computational Modeling

Background:

The center of body mass (COM) is crucial for evaluating human postural control and stability.
Current methods for COM estimation are often not accessible for routine clinical assessment, hindering the evaluation of balance problems.

Purpose of the Study:

To develop a novel hybrid genetic algorithm sum-of-sines model for estimating the center of body mass (COM) trajectory.
To create an accessible and portable system for COM estimation applicable in clinical settings.

Main Methods:

A hybrid genetic algorithm sum-of-sines model was developed.
The model utilizes input data from two portable accelerometers.
The model's performance was evaluated for COM trajectory estimation.

Main Results:

The developed model demonstrated promising results in estimating the center of body mass (COM) trajectory.
The use of accelerometers provides an inexpensive and user-friendly data acquisition method.

Conclusions:

The hybrid genetic algorithm sum-of-sines model offers a viable approach for estimating COM trajectory.
This method has potential clinical applications for assessing balance and postural control issues.
The system's portability and low cost enhance its suitability for routine clinical use.