![]() ![]() Lie slightly below the level of the surrounding plains. By dividing the moment of inertia by the total mass of the planet M and the total radius squared R2, the result is the part of the moment of inertia that is due entirely to radial changes in density in the planet. To compare moments of inertia among planets, scientists calculate what is called the moment of inertia factor. Where rg is the center of the planet and r is the total radius of the planet, p(r) is the change of density with radius in the planet, and r is the radius of the planet and the variable of integration. In a planet, the density changes with radius, and so the moment of inertia needs to be calculated with an integral: The units of the moment of inertia are units of mass times distance squared for example, lb X ft2 or kg X m2.īy definition, the moment of inertia I is defined as the sum of mr2 for every piece of mass m of the object, where r is the radius for that mass m. The bicycle wheel has the greater moment of inertia and takes more force to create the same angular acceleration. This is similar to an example of two wheels with the same mass: one is a solid plate and the other is a bicycle wheel, with almost all the mass at the rim. In other words, if all the mass is at the outside, it takes more force to spin the planet than if all the mass is at the center. The farther the bulk of the mass is from the center of the planet, the greater the moment of inertia. The moment of inertia depends on the mass of the planet and on how this mass is distributed around the planet's center. (In more technical terms, the angular acceleration of an object is proportional to the torque acting on the object, and the proportional constant is called the moment of inertia of the object.) It is denoted by K.The moment of inertia of a planet is a measure of how much force is required to increase the spin of the planet. The radius of gyration of a body is the perpendicular to distance from the axis of rotation to the point at which the moment of inertia obtained by taking the total mass of the body as the center is equal to the actual moment of inertia of the object. Uniform Plate or Rectangular Parallelepiped I = ∑m ir i 2 Moment Of Inertia of Some Common ObjectsĮxpressions for the moment of inertia for some symmetric objects along with their axis of rotation are discussed below in this table.
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