By Wilhelm H Westphal

This booklet is a translation of the sixth to eighth version of the author's Kleines Lehrbuch der Physik. The circle of readers to which it hopes to charm and the author's goal in writing it were set out within the Preface to the 1st German version, released in 1948. the current publication continuously follows the foundations of the speculation of amounts, the beginnings of which date again to James C. Maxwell. which means in all equations during this publication the symbols perpetually stand for actual amounts and never for the numerical values of amounts. merely then are the equations gene rally legitimate and autonomous of the alternative of devices utilized in their assessment. The devices used are regularly the "metric" devices that have been gaining floor more and more additionally within the English-speaking nations. A conversion desk for a number of the extra very important Anglo-American devices is given on web page XIV. i need to checklist my honest gratitude to Mr. Ewald Osers for his pains taking paintings in making this translation and to Mr. P. C. Banbury, Ph. D., of the dep. of Physics, college of examining, England, either for the recommendation he has given hirn all through and for devising the issues especially for this version.

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The circular pendulum: (a) observer at rest; (b) observer participating in rotation 37 32. Centrifugal force We will now consider a circular pendulum (Fig. 29a) which we picture as consisting of a point mass m suspended from a mass-Iess string of length land moving along a circular path of radius r. Let the displacement of the pendulum from its position of equilibrium be 0(, so that r = I sin 0(. 'h tr2 points in the direction of the string and is balanced by a reactive force trr brought into play in the string.

To the height h- y. To bring ab out this state of affairs from the outset the amount of work needed for the first body would have been only mg(h - y) instead of mg h; the amount of work needed for the second body would have been mg y. In order to raise the first body to the height h the work mg y had to be done on it additionaIly. This work done on it along the distance y is exactIy the work done in raising the second body. In dropping along the distance y the first body therefore transferred to the second that precise amount of its stored-up work, its potential energy, which had been done on it along the same distance earlier.

At the time t=vo/g (rise time) its velocity v = O. e. 2), is v= -Vo. Rise and fall therefore are symmetrical in time. 2) we have for the velocity at altitude y: v2 =v~-2g y=2g(h- y). 4) Let us now suppose that a body is projected obliquely upward with an initial velocity Vo at an angle ljJ with the horizontal from a point x = 0, y = O. o = Vo cos ljJ and vy,o = V o sin ljJ (Fig. 22a). x Fig. 22. a and b parabolic trajectories; c ballistic curve horizontal and a vertical motion. In the direction x the body is not acted upon by any force.