The Principles of Mechanics; An Elementary Exposition for Students of Physics Volume 1-2

The Principles of Mechanics; An Elementary Exposition for Students of Physics Volume 1-2

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This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1911 edition. Excerpt: ... and T'1 being found by observation, equations (2) and (3) yield values for I, and k. 95. The ordinary form of clock pendulum is essentially a rigid body rotating about a fixed horizontal axis under the influence of its weight. In order to determine the most important characteristics of the motion of such a weight pendulum, we shall eliminate from consideration all secondary elements of the problem. These may be introduced afterward to any extent desired, as "corrections" applied to the main result. Let the diagram (Fig. 22) represent a vertical section of the body, perpendicular to the horizontal rotation-axis shown at O, and containing the centre of mass C. The point 0 is commonly known as the centre of suspension; it shall be the origin, X being drawn vertically downward. The mass of the body is m; Fm 22 the distance 0C is F; and the angle-y (COX) is measured from the equilib rium position of C. The total moment of the weight is--m, gF silly ( 85), and the general equation ((1), 73) adapted to this special case becomes The angular velocity at any position can be obtained by direct integration of (1), writing % for %; or the work equation ((2), 68) can be applied. By either method the result is the initial conditions being y= 70, w = w0. In discussing pendulum motion it. is usually convenient to choose 1.00:0 at t = 0, in which case 'yo is the (angular) amplitude. A prominent element connected with pendulums is the time between successive positions of rest, the time of one heat. In the present instance the exact integration of equation (2), that would determine y as a function of t, is impossible. A process of approximation being necessary, it may be begun at equation (1), which would be of harmonic...
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Product details

  • Paperback | 80 pages
  • 189 x 246 x 4mm | 159g
  • United States
  • English
  • black & white illustrations
  • 1236822463
  • 9781236822468