To answer this question we have to employ the other extremely simple law, which I said I must explain to you. It is this: The acceleration and the force vary in a constant ratio with each other. Thus, let force 1 produce acceleration 1, then force 1 applied again will produce acceleration 1 again, or, in other words, force 2 will produce acceleration 2, and so on. This being so, and the amount of the deflection varying as the squares of the speeds in the two cases, the centrifugal force of a body making one revolution per minute in a circle of
1²
one foot radius will be ---------- = 0.000341
54.166²
--the coefficient of centrifugal force.
There is another mode of making this computation, which is rather neater and more expeditious than the above. A body making one revolution per minute in a circle of one foot radius will in one second revolve through an arc of 6°. The versed sine of this arc of 6° is 0.0054781046 of a foot. This is, therefore, the distance through which a body revolving at this rate will be deflected in one second. If it were acted on by a force equal to its weight, it would be deflected through the distance of 16.083 feet in the same time. What is the deflecting force actually exerted upon it? Of
0.0054781046
course, it is ------------.
16.083
This division gives 0.000341 of its weight as such deflecting force, the same as before.
In taking the versed sine of 6°, a minute error is involved, though not one large enough to change the last figure in the above quotient. The law of uniform acceleration does not quite hold when we come to an angle so large as 6°. If closer accuracy is demanded, we can attain it, by taking the versed sine for 1°, and multiplying this by 6². This gives as a product 0.0054829728, which is a little larger than the versed sine of 6°.
I hope I have now kept my promise, and made it clear how the coefficient of centrifugal force may be found in this simple way.
We have now learned several things about centrifugal force. Let me recapitulate. We have learned:
1st. The real nature of centrifugal force. That in the dynamical sense of the term force, this is not a force at all: that it is not capable of producing motion, that the force which is really exerted on a revolving body is the centripetal force, and what we are taught to call centrifugal force is nothing but the resistance which a revolving body opposes to this force, precisely like any other resistance.