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The center of mass of a body with an axis of symmetry and constant density must lie on this axis. Thus, the center of mass of a circular cylinder of constant density has its center of mass on the axis of the cylinder. In the same way, the center of mass of a spherically symmetric body of constant density is at the center of the sphere.
Solid paraboloid of revolution around z-axis: a = the radius of the base circle h = the height of the paboloid from the base cicle's center to the edge Solid ellipsoid: a, b, c = the principal semi-axes of the ellipsoid
Hume-Rothery rules, named after William Hume-Rothery, are a set of basic rules that describe the conditions under which an element could dissolve in a metal, forming a solid solution. There are two sets of rules; one refers to substitutional solid solutions, and the other refers to interstitial solid solutions.
a point such that the translational motion is zero or simplified, e.g. on an axle or hinge, at the center of a ball and socket joint, etc. When the center of mass is used as reference point: The (linear) momentum is independent of the rotational motion. At any time it is equal to the total mass of the rigid body times the translational velocity.
A solid, spherically symmetric body can be modeled as an infinite number of concentric, infinitesimally thin spherical shells. If one of these shells can be treated as a point mass, then a system of shells (i.e. the sphere) can also be treated as a point mass. Consider one such shell (the diagram shows a cross-section):
The centroid of a solid hemisphere (i.e. half of a solid ball) divides the line segment connecting the sphere's center to the hemisphere's pole in the ratio : (i.e. it lies of the way from the center to the pole). The centroid of a hollow hemisphere (i.e. half of a hollow sphere) divides the line segment connecting the sphere's center to the ...
In particular, a non-uniform gravitational field can produce a torque on an object, even about an axis through the center of mass. The center of gravity seeks to explain this effect. Formally, a center of gravity is an application point of the resultant gravitational force on the body. Such a point may not exist, and if it exists, it is not unique.
There are two forces; one is the force of gravity vertically downward through the center of mass of the ball mg, where m is the mass of the ball and g is the gravitational acceleration; the second is the upward normal force exerted by the road at a right angle to the road surface ma n. The centripetal force demanded by the curved motion is also ...