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where I s is the moment of inertia, ω s is the angular velocity of spin about the spin axis, m is the mass, g is the acceleration due to gravity, θ is the angle between the spin axis and the axis of precession and r is the distance between the center of mass and the pivot. The torque vector originates at the center of mass.
Mathematically, the moment of inertia of a simple pendulum is the ratio of the torque due to gravity about the pivot of a pendulum to its angular acceleration about that pivot point. For a simple pendulum, this is found to be the product of the mass of the particle m {\displaystyle m} with the square of its distance r {\displaystyle r} to the ...
Earth's rotation axis moves with respect to the fixed stars (inertial space); the components of this motion are precession and nutation. It also moves with respect to Earth's crust; this is called polar motion. Precession is a rotation of Earth's rotation axis, caused primarily by external torques from the gravity of the Sun, Moon and other bodies.
As the Earth has a sidereal rotation period of 23.93 hours, it has an angular velocity of 7.29 × 10 −5 rad·s −1. [2] The Earth has a moment of inertia, I = 8.04 × 10 37 kg·m 2. [3] Therefore, it has a rotational kinetic energy of 2.14 × 10 29 J. Part of the Earth's rotational energy can also be tapped using tidal power.
The rotation has caused the planet to settle on a spheroid shape, such that the normal force, the gravitational force and the centrifugal force exactly balance each other on a "horizontal" surface. (See equatorial bulge.) The Coriolis effect caused by the rotation of the Earth can be seen indirectly through the motion of a Foucault pendulum.
At a fixed point on the surface, the magnitude of Earth's gravity results from combined effect of gravitation and the centrifugal force from Earth's rotation. [ 2 ] [ 3 ] At different points on Earth's surface, the free fall acceleration ranges from 9.764 to 9.834 m/s 2 (32.03 to 32.26 ft/s 2 ), [ 4 ] depending on altitude , latitude , and ...
Inertia is the natural tendency of objects in motion to stay in motion and objects at rest to stay at rest, unless a force causes the velocity to change. It is one of the fundamental principles in classical physics, and described by Isaac Newton in his first law of motion (also known as The Principle of Inertia). [1]
Axial precessional movement. Axial precession is the trend in the direction of the Earth's axis of rotation relative to the fixed stars, with a period of about 25,700 years. Also known as the precession of the equinoxes, this motion means that eventually Polaris will no longer be the north pole star.