Читать книгу The Modern Clock. A Study of Time Keeping Mechanism; Its Construction, Regulation and Repair онлайн

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Fig. 1. Dotted lines show path of pendulum.

The next forces to consider are mass and weight, which, when put in motion, tend to continue that motion indefinitely unless brought to rest by other forces opposing it. This is known as momentum. A heavy bob will swing longer than a light one, because the momentum stored up during its fall will be greater in proportion to the resistance which it encounters from the air and the suspension spring.

As the length of the rod governs the distance through which our bob is allowed to fall, and also controls the direction of its motion, we must consider this motion. Referring again to ssss1, we see that the bob moves along the circumference of a circle, with the rod acting as the radius of that circle; this opens up another series of facts. The circumference of a circle equals 3.1416 times its diameter, and the radius is half the diameter (the radius in this case being the pendulum rod). The areas of circles are proportional to the squares of their diameters and the circumferences are also proportional to their areas. Hence, the lengths of the paths of bobs moving along these circumferences are in proportion to the squares of the lengths of the pendulum rods. This is why a pendulum of half the length will oscillate four times as fast.