the energy of earth's rotation is an example of hamiltonian mechanics.
the energy of earth's rotation is an example of hamiltonian mechanics.
the energy of earth's rotation is an example of?
hamiltonian mechanics
because the earth's tides are ultimately due to gravitational interaction with the moon and sun and the earth's rotation, tidal power is practically inexhaustible and classified as a renewable energy resource. movement of tides causes a loss of mechanical energy in the earth–moon system: this is a result of pumping of water through natural restrictions around coastlines and consequent viscous dissipation at the seabed and in turbulence. this loss of energy has caused the rotation of the earth to slow in the 4.5 billion years since its formation. during the last 620 million years the period of rotation of the earth (length of a day) has increased from 21.9 hours to 24 hours; in this period the earth has lost 17% of its rotational energy. while tidal power will take additional energy from the system, the effect is negligible and would only be noticed over millions of years.
tidal power
the gravitational torque between the moon and the tidal bulge of earth causes the moon to be constantly promoted to a slightly higher orbit and earth to be decelerated in its rotation. as in any physical process within an isolated system, total energy and angular momentum are conserved. effectively, energy and angular momentum are transferred from the rotation of earth to the orbital motion of the moon (however, most of the energy lost by earth (−3.321 tw) is converted to heat by frictional losses in the oceans and their interaction with the solid earth, and only about 1/30th (+0.121 tw) is transferred to the moon). the moon moves farther away from earth (+38.247±0.004 mm/y), so its potential energy (in earth's gravity well) increases. it stays in orbit, and from kepler's 3rd law it follows that its angular velocity actually decreases, so the tidal action on the moon actually causes an angular deceleration, i.e. a negative acceleration (−25.858±0.003"/century) of its rotation around earth. the actual speed of the moon also decreases. although its kinetic energy decreases, its potential energy increases by a larger amount.
tidal acceleration