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Diagram of an educational toy that balances on a point: the center of mass (C) settles below its support (P) A body's center of gravity is the point around which the resultant torque due to gravity forces vanishes. [13] Where a gravity field can be considered to be uniform, the mass-center and the center-of-gravity will be the same.
The following is a list of centroids of various two-dimensional and three-dimensional objects. The centroid of an object in -dimensional space is the intersection of all hyperplanes that divide into two parts of equal moment about the hyperplane.
In physics, if variations in gravity are considered, then a center of gravity can be defined as the weighted mean of all points weighted by their specific weight. In geography , the centroid of a radial projection of a region of the Earth's surface to sea level is the region's geographical center .
Two common methods for finding the volume of a solid of revolution are the disc method and the shell method of integration.To apply these methods, it is easiest to draw the graph in question; identify the area that is to be revolved about the axis of revolution; determine the volume of either a disc-shaped slice of the solid, with thickness δx, or a cylindrical shell of width δx; and then ...
In a molecule that also has an axis of symmetry, a mirror plane that includes the axis is called a vertical mirror plane and is labeled σ v, while one perpendicular to the axis is called a horizontal mirror plane and is labeled σ h. A vertical mirror plane that bisects the angle between two C2 axes is called a dihedral mirror plane, σ d. [6]
In classical mechanics, the stretch rule (sometimes referred to as Routh's rule) states that the moment of inertia of a rigid object is unchanged when the object is stretched parallel to an axis of rotation that is a principal axis, provided that the distribution of mass remains unchanged except in the direction parallel to the axis. [1]
Here, the function gives the mass density at each point (,,), is a vector perpendicular to the axis of rotation and extending from a point on the rotation axis to a point (,,) in the solid, and the integration is evaluated over the volume of the body . The moment of inertia of a flat surface is similar with the mass density being replaced by ...
The special case of circular orbits is an example of a rotation around a fixed axis: this axis is the line through the center of mass perpendicular to the plane of motion. The centripetal force is provided by gravity, see also two-body problem. This usually also applies for a spinning celestial body, so it need not be solid to keep together ...