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Hollow sphere of radius r and mass m. = [1] Solid sphere of radius r and mass m. = [1] Sphere (shell) of radius r 2 and mass m, with centered spherical cavity of radius r 1. When the cavity radius r 1 = 0, the object is a solid ball (above).
Propositions 70 and 71 consider the force acting on a particle from a hollow sphere with an infinitesimally thin surface, whose mass density is constant over the surface. The force on the particle from a small area of the surface of the sphere is proportional to the mass of the area and inversely as the square of its distance from the particle.
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.
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 ...
The Sun has by far the lowest moment of inertia factor value among Solar System bodies; it has by far the highest central density (162 g/cm 3, [3] [note 3] compared to ~13 for Earth [4] [5]) and a relatively low average density (1.41 g/cm 3 versus 5.5 for Earth).
This is determined by summing the moments of inertia of the thin discs that can form the sphere whose centers are along the axis chosen for consideration. If the surface of the sphere is defined by the equation [ 23 ] : 1301 x 2 + y 2 + z 2 = R 2 , {\displaystyle x^{2}+y^{2}+z^{2}=R^{2},}
For example, assuming the Earth is a sphere of radius 6371 km, the surface area of the arctic (north of the Arctic Circle, at latitude 66.56° as of August 2016 [7]) is 2π ⋅ 6371 2 | sin 90° − sin 66.56° | = 21.04 million km 2 (8.12 million sq mi), or 0.5 ⋅ | sin 90° − sin 66.56° | = 4.125% of the total surface area of the Earth.
Sphere packing finds practical application in the stacking of cannonballs. In geometry, a sphere packing is an arrangement of non-overlapping spheres within a containing space. The spheres considered are usually all of identical size, and the space is usually three-dimensional Euclidean space.