CENTRAL FORCES. The two antagonist forces by which bodies are caused to revolve round a central point. As all forces act in right lines, the tendency of any body moving in a circle is to fly off in a right line forming a tangent to the circle, and this tendency is called the centrifugal force ; and the force by which it is restrained from so flying off, and which maintains it in its curvilinear path, is termed the centripetal force; and these two forces are necessarily equal to each other. Dr. Brewster has summed up the whole doctrine of the central forces in the following propositions. 1. The centrifugal forces of two unequal bodies moving with the same velocity, and at the same distance from the centre of motion, are to one another as the respective quantities of matter in the two bodies. 2. The centrifugal forces of two equal bodies which perform their revolutions round the central body in the same time, but at different distances from it, are to one another as their respective distances from the central body. 3. The centrifugal forces of two bodies which perform their revolutions in the same time, and whose quantities of matter are inversely as their distances from the centre, are equal to each other. 4. The centrifugal force of two equal bodies moving at the same distance from the central body, but with different velocities, are to one another as the squares of the velocities. 5. The centrifugal forces of two unequal bodies moving at equal distances from the centre with different velocities, are to one another in the compound ratio of their quantities of matter and the squares of their velocities. 6. The centrifugal forces of two equal, bodies moving with equal velocities at different distances from the centre, are inversely as their distances from the centre. 7. The
centrifugal forces of two unequal bodies moving with equal velocities at different distances from the centre, are to one another as their quantities of matter multiplied oy their respective distances from the centre. 8. The centrifugal forces of two unequal bodies moving with unequal velocities at different dis tances from the centre, are in the compound ratio of their quantities of matter, the squares of their velocities, and their distances from the centre.
To find the centrifugal force of any body :—Divide the velocity in feet per second by 4.01, and the square of the quotient by the diameter of the circle ; the quotient is the centrifugal force when the weight of the body is 1. Hence the quotient, multiplied by the weight of the body, is the cen force .
required.—Ex. Required the centrifugal force of the rim of a ;0 feet in diameter, moving with a velocity of 34 feet per second: 34+4.01=8.02 and 8.02r+20=3.216 times the weight e 1-,e rim.
Rule 2.—Multiply the square of the number of revolutions per minute, by the diameter of the circle in feet, and divide the product by the constant number 5870, and the quotient is the centrifugal force when the weight of the body is 1 ; and this quotient, multiplied by the weight of the body, is its centrifugal force. Ex. Required the centrifugal force of a stone weighing 2 lbs., revolving in a circle of 4 feet diameter, at the rate of 120 revolutions per minute : hence 9.81 x 2=19.62 centrifugal force.