among the endless possible motions of matter, periodic motion plays a particularly important role, not only because it occurs so widely in nature and everyday life, in man as well as machine, from the beat of the pulse to the motion of the planets, but also because of its basic role in physics; the concept and measurement of time are intimately linked to it.
a periodic motion of a particle is one which repeats itself over and over again. the motion is bounded, which means that it is confined to a finite region of space. this confinement is the result of the interaction of the particle with other particles, including matter in bulk. thus, in planetary motion the interaction force on it is the collective effect of all the water 'particles'.
the periodic motions of the moon and the planets have played important roles in the development of physics. kepler's discovery that the planetary orbits are elliptical with the sun at the focus, that the sector velocity of the planet is constant, and that the period is proportional to the 3/2 power of the major axis of the orbit, supported the hypothesis that the gravitational force is central and varies as the inverse square of the sun-planet distance.
another important example is the motion of a charged particle in a unuform magnetic field. in a plane normal to the magnetic field, the orbit will be circular with constant speed, and if the particle has a magnetic moment, it will also precess with a frequency proportional to the magnetic field. when applied to the nucleus, the measurement of this precession or gyro frequency is often used as a means of measuring the magnetic field.
a periodic motion of a particle is one which repeats itself over and over again. the motion is bounded, which means that it is confined to a finite region of space. this confinement is the result of the interaction of the particle with other particles, including matter in bulk. thus, in planetary motion the interaction force on it is the collective effect of all the water 'particles'.
the periodic motions of the moon and the planets have played important roles in the development of physics. kepler's discovery that the planetary orbits are elliptical with the sun at the focus, that the sector velocity of the planet is constant, and that the period is proportional to the 3/2 power of the major axis of the orbit, supported the hypothesis that the gravitational force is central and varies as the inverse square of the sun-planet distance.
another important example is the motion of a charged particle in a unuform magnetic field. in a plane normal to the magnetic field, the orbit will be circular with constant speed, and if the particle has a magnetic moment, it will also precess with a frequency proportional to the magnetic field. when applied to the nucleus, the measurement of this precession or gyro frequency is often used as a means of measuring the magnetic field.
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