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The total kinetic energy of a system depends on the inertial frame of reference: it is the sum of the total kinetic energy in a center of momentum frame and the kinetic energy the total mass would have if it were concentrated in the center of mass.
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.
Kinetic energy is the energy of motion. The amount of translational kinetic energy found in two variables: the mass of the object and the speed of the object as shown in the equation above. Kinetic energy must always be either zero or a positive value.
The total translational kinetic energy of the gas is defined as =, providing the result =. This is an important, non-trivial result of the kinetic theory because it relates pressure, a macroscopic property, to the translational kinetic energy of the molecules, which is a microscopic property.
The second part expresses the kinetic energy of a system of particles in terms of the velocities of the individual particles and the centre of mass.. Specifically, it states that the kinetic energy of a system of particles is the sum of the kinetic energy associated to the movement of the center of mass and the kinetic energy associated to the movement of the particles relative to the center ...
The Hamiltonian of a system represents the total energy of the system; that is, the sum of the kinetic and potential energies of all particles associated with the system. . The Hamiltonian takes different forms and can be simplified in some cases by taking into account the concrete characteristics of the system under analysis, such as single or several particles in the system, interaction ...
The first term in the above nuclear wave function equation corresponds to kinetic energy of nuclei due to their radial motion. Term Φ s | N 2 |Φ s / 2μR 2 represents rotational kinetic energy of the two nuclei, about their center of mass, in a given electronic state Φ s. Possible values of the same are different rotational energy ...
The net external force on the rigid body is always equal to the total mass times the translational acceleration (i.e., Newton's second law holds for the translational motion, even when the net external torque is nonzero, and/or the body rotates). The total kinetic energy is simply the sum of translational and rotational energy.