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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.
A polyatomic gas, like water, is not radially symmetric about any axis, resulting in D = 6, comprising 3 translational and 3 rotational degrees of freedom. Because the equipartition theorem requires that kinetic energy is partitioned equally, the total kinetic energy is = =.
E k is the total kinetic energy; 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.
Thermal (kinetic) energy added to a gas or liquid (an endothermic process) produces translational, rotational, and vibrational motion. In contrast, a solid can only increase its internal energy by exciting additional vibrational modes, as the crystal lattice structure prevents both translational and rotational motion.
The (Newtonian) kinetic energy of a particle of mass m, velocity v is given by = | | = (+ +), where v x, v y and v z are the Cartesian components of the velocity v.Here, H is short for Hamiltonian, and used henceforth as a symbol for energy because the Hamiltonian formalism plays a central role in the most general form of the equipartition theorem.
For example, the sum of translational and rotational kinetic and potential energy within a system is referred to as mechanical energy, whereas nuclear energy refers to the combined potentials within an atomic nucleus from either the nuclear force or the weak force, among other examples. [3]
Energy. kinetic; potential; Force; Frame of reference; ... the Newton–Euler equations describe the combined translational and rotational dynamics of a rigid body ...
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.