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The rigid body's motion is entirely determined by the motion of its inertia ellipsoid, which is rigidly fixed to the rigid body like a coordinate frame. Its inertia ellipsoid rolls, without slipping, on the invariable plane , with the center of the ellipsoid a constant height above the plane.
The spheroidal shape of the Earth is the result of the interplay between gravity and centrifugal force caused by the Earth's rotation about its axis. [18] [19] In his Principia, Newton proposed the equilibrium shape of a homogeneous rotating Earth was a rotational ellipsoid with a flattening f given by 1/230.
A set of equations describing the trajectories of objects subject to a constant gravitational force under normal Earth-bound conditions.Assuming constant acceleration g due to Earth's gravity, Newton's law of universal gravitation simplifies to F = mg, where F is the force exerted on a mass m by the Earth's gravitational field of strength g.
The moments of inertia of a mass have units of dimension ML 2 ([mass] × [length] 2). It should not be confused with the second moment of area, which has units of dimension L 4 ([length] 4) and is used in beam calculations. The mass moment of inertia is often also known as the rotational inertia, and sometimes as the angular mass.
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Assuming that the Earth was a completely rigid body, they calculated the period of Earth’s polhode wobble to be about 9–10 months. [ citation needed ] During the mid 19th century, Louis Poinsot developed a geometric interpretation of the physics of rotating bodies that provided a visual counterpart to Euler’s algebraic equations.