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The principle of classical mechanics that E ∝ mv 2 is conserved was first developed by Gottfried Leibniz and Johann Bernoulli, who described kinetic energy as the living force or vis viva. [4]: 227 Willem 's Gravesande of the Netherlands provided experimental evidence of this relationship in 1722. By dropping weights from different heights ...
Every degree of freedom in the energy is quadratic and, thus, should contribute 1 ⁄ 2 k B T to the total average energy, and 1 ⁄ 2 k B to the heat capacity. Therefore, the heat capacity of a gas of N diatomic molecules is predicted to be 7N· 1 ⁄ 2 k B: the momenta p 1 and p 2 contribute three degrees of freedom each, and the extension q ...
newton meter squared per kilogram squared (N⋅m 2 /kg 2) shear modulus: pascal (Pa) or newton per square meter (N/m 2) gluon field strength tensor: inverse length squared (1/m 2) acceleration due to gravity: meters per second squared (m/s 2), or equivalently, newtons per kilogram (N/kg) magnetic field strength
If the body's speed v is much less than c, then reduces to E = 1 / 2 m 0 v 2 + m 0 c 2; that is, the body's total energy is simply its classical kinetic energy ( 1 / 2 m 0 v 2) plus its rest energy.
The formula defines the energy E of a particle in its rest frame as the product of mass (m) with the speed of light squared (c 2). Because the speed of light is a large number in everyday units (approximately 300 000 km/s or 186 000 mi/s), the formula implies that a small amount of mass corresponds to an enormous amount of energy.
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.
Consider N = 2 particles with equal mass m, acted upon by mutually attractive forces. Suppose the particles are at diametrically opposite points of a circular orbit with radius r. The velocities are v 1 (t) and v 2 (t) = −v 1 (t), which are normal to forces F 1 (t) and F 2 (t) = −F 1 (t). The respective magnitudes are fixed at v and F.
[nb 2] [8] It is defined as one half the product of the object's mass with the square of its speed, and the total kinetic energy of a system of objects is the sum of the kinetic energies of the respective objects: [1] [9] =