Experimental Mechanics / A Course of Lectures Delivered at the Royal College of Science for Ireland

by Robert S. Ball

Fig. 74.

A small toothed wheel is mounted on the same socket as c; this is behind p q, and is therefore not seen in the figure: the whole is made to revolve rapidly by the large wheel e, which is turned by the handle d.

560. The room being darkened, a beam from the lime-light is allowed to fall on the apparatus: the reflections of the light are seen in the two silvered balls as two bright points. When d is turned, the balls move round rapidly, and you see the points of light reflected from them describe circles. The ball b when at rest is 4" from c, while a is 8" from c; hence the circle described by b is smaller than that described by a. The appearance presented is that of two concentric luminous circles. As the speed increases, the inner circle enlarges till the two circles blend into one. By increasing the speed still more, you see the circle whose diameter is enlarging actually exceeding the fixed circle, and its size continues to increase until the highest velocity which it is safe to employ has been communicated to the machine.

561. What is the explanation of this? The arm a is fixed and the distance a c cannot alter, hence a describes the fixed circle. b, on the other hand, is not fixed; it can recede from c, and we find that the quicker the speed the further it recedes. The larger the circle described by b the more is the spring stretched, and the greater is the force with which b is attracted towards the centre. This experiment proves that the force necessary to retain a body in a circular path must be increased when the speed is increased.

562. Thus we see that uniform motion of a body in a circle can only be produced by an uniform force directed to the centre.

If the motion, even though circular, have variable speed the law of the force is not so simple.

563. We can measure the magnitude of this force by the same apparatus. The ball b weighs 0·1 lb. I find that I must pull it with a force of 3 lbs. in order to draw it to a distance of 8" from c; that is, to the same distance as a is from c. Hence, when the diameters of the circles in which the balls move are equal, the central force must be 3 lbs.; that is, it must be nearly thirty times as great as gravity.

564. The necessity for the central force is thus shown: Let us conceive a weight attached to a string to be swung round in a circle, a portion of which is shown in [Fig. 75].

Fig. 75.