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An example is the calculation of the rotational kinetic energy of the Earth. 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.
In classical mechanics, Euler's rotation equations are a vectorial quasilinear first-order ordinary differential equation describing the rotation of a rigid body, using a rotating reference frame with angular velocity ω whose axes are fixed to the body.
The trivial case of the angular momentum of a body in an orbit is given by = where is the mass of the orbiting object, is the orbit's frequency and is the orbit's radius.. The angular momentum of a uniform rigid sphere rotating around its axis, instead, is given by = where is the sphere's mass, is the frequency of rotation and is the sphere's radius.
E t is the translational kinetic energy; E r is the rotational energy or angular kinetic energy in the rest frame; Thus the kinetic energy of a tennis ball in flight is the kinetic energy due to its rotation, plus the kinetic energy due to its translation.
In the physical science of dynamics, rigid-body dynamics studies the movement of systems of interconnected bodies under the action of external forces.The assumption that the bodies are rigid (i.e. they do not deform under the action of applied forces) simplifies analysis, by reducing the parameters that describe the configuration of the system to the translation and rotation of reference ...
An arbitrarily shaped rigid rotor is a rigid body of arbitrary shape with its center of mass fixed (or in uniform rectilinear motion) in field-free space R 3, so that its energy consists only of rotational kinetic energy (and possibly constant translational energy that can be ignored).
Much of this energy is reradiated back to the surface in the infrared through the "greenhouse effect." Because room temperature (≈298 K) is over the typical rotational temperature but lower than the typical vibrational temperature, only the translational and rotational degrees of freedom contribute, in equal amounts, to the heat capacity ratio.
Rotational or angular kinematics is the description of the rotation of an object. [21] In what follows, attention is restricted to simple rotation about an axis of fixed orientation. The z -axis has been chosen for convenience.