mass moment of inertia for a solid sphere:
I = (2 /5) * mass * radius2
(mass in kg, radius in metres)
the moment of inertia of a solid cylinder about an axis passing through its COM and parallel to its length is mr2/2 where r is the radius.
A sphere is a geometric solid because it has 3 dimentions.
A sphere is a solid with no edges.
Sphere ,because the sphere is roll if you put sphere in the table it can be roll. *_*
sphere
Rotated about a line on the surface ? I = Mass * radius2 . Rotated about a line through the centre : I = (2 * mass * radius2) / 5
the moment of inertia of a solid cylinder about an axis passing through its COM and parallel to its length is mr2/2 where r is the radius.
2/5 mr2
Moment of inertia depends upon the distribution of mass with respect to the axis of rotation.The greater the distance between the bulk of an object's mass and the axis of rotation, the greater the moment of inertia will be. A solid disk has its mass distributed evenly across its diameter, while a ring has its mass concentrated furthest from the centre of rotation.
The disk because it has a lower moment of inertia for a given mass.
An object rotating about its long axis will have a different moment of inertia than when it is rotating about its short axis. A solid disk will have a different moment than a washer, and there are formulas derived for calculating the moments of many common shapes.
Since a sphere is round it is a shape without a face.
No it is not a solid.
A sphere is a geometric solid because it has 3 dimentions.
sphere
Think of it as the difference in moment of inertias for two solid cubes. Calculate the moment of inertia of a solid cube with dimensions equal to the inner dimensions of your hollow cube. Then calculate the moment of inertia of a solid cube with dimensions equal to the outer dimensions of your hollow cube. Subtract the moment of inertia of the inner dimensions from the moment of inertia of the outer dimensions to get the moment of inertia of what's left. Same concept applies to finding the area of a thin-walled circle. Outer area - inner area = total area. Outer moment of inertia - inner moment of inertia = total moment of inertia. This approach won't work however if you're considering hollow shell - a cube with walls of zero thickness. If the axis of rotation goes through the cube center, perpendicular to one of its walls, first calculate moment of inertia of the wall that the axis passes through (let's call it Ia). For all equations below d equals surface density(mass per unit of area) and a is length of cube's side. Ia= d * a4 / 6 Then you have to calculate moments of inertia of four walls parallel to the axis. This will be Ib=4 * Iwall=4*d*a4/3. Total moment of the shell will be then: I=2*Ia+Ib=1.5*d*a4. If the axis is through the center and ┴ one face, I = (m/6)*[a² - (a-t)²], or I = (m/6)(2at - t²) for any value of t, however small. Source: CRC Std Math Tables
the indivisible solid sphere was invented in 1803 by John Dalton