Login-Verarbeitung ...

Trial ends in Request Full Access Tell Your Colleague About Jove

9.3: Centroid of a Body

JoVE Core
Mechanical Engineering

Ein Abonnement für JoVE ist erforderlich, um diesen Inhalt ansehen zu können. Melden Sie sich an oder starten Sie Ihre kostenlose Testversion.

Centroid of a Body

9.3: Centroid of a Body

The centroid is an important concept in engineering, physics, and mechanics. It is the geometric center of a body. It always lies within the body except in cases with holes or cavities. When the material that a body is composed of is uniform or homogeneous, the centroid coincides with its center of mass or the center of gravity.

For a homogeneous body with constant density, the centroid can usually be found using equations representing a balance of the moments of the body's volume. If the volume has two planes of symmetry, then the centroid must lie along the line of intersection between those two planes. Additionally, for areas lying in an x-y plane bounded by a curve, this calculation for obtaining the coordinates for centroidal location can be done using a rectangular strip for the differential area element, and then integrating it. Similarly, the centroid can also be obtained for a line segment on an x-y plane described by a thin curve y = f (x). The centroidal coordinates for a line is determined using the following expressions:

Equation 1

The knowledge of the location of the centroid of a body helps to calculate moments of inertia and other important properties in physics and mechanics. Knowing these properties helps engineers design stable structures that can withstand various loads without buckling and other problems that may arise during their lifetime.

Suggested Reading


Centroid Engineering Physics Mechanics Geometric Center Body Uniform Homogeneous Center Of Mass Center Of Gravity Balance Of Moments Planes Of Symmetry Intersection Coordinates Moments Of Inertia Stable Structures

Get cutting-edge science videos from JoVE sent straight to your inbox every month.

Waiting X
Simple Hit Counter