LAWS OF CENTRIFUGAL FORCE. 143 



The preceding experiments have proved that the 

 centrifugal force increases with the weight of the rota- 

 ting body and also with its distance from the axis of 

 rotation; the force is directly proportional to these two 

 magnitudes. A body three times as heavy as another 

 body has three times as great a centrifugal force, 

 if all other conditions are the same; a body five times 

 as far away from the centre as another, has five 

 times as great a centrifugal force, if the time occupied 

 by one rotation is the same for both. 



We have further seen that the centrifugal force 

 becomes greater, if the velocity of rotation increases ; 

 but it is not simply proportional to the speed. If the 

 velocity is doubled, that is, if the time of rotation 

 becomes half of what it was before, the centrifugal 

 force becomes four times as great; if the velocity is 

 trebled, the centrifugal force is nine times as great: 

 in other words, the centrifugal force is directly 

 proportional to the square of the velocity. 1 



A practical application of centrifugal force is seen in 

 the governor of a steam-engine. This consists of two 

 heavy balls suspended by rods which are hinged to 



vertical shaft. Motion is imparted to this by means 



1 The centrifugal force of a body moving in a circle is found by multi- 

 plying its weight by its distance from the axis of rotation, expressed in 

 netres, and by the number 4*025, and dividing the product by the square 

 >f the number of seconds required for one revolution. Thus a stone weigh - 

 ng 400* r , attached to a string l m> 5 long, and whirled round once in 2 s , has a 

 entrifugal force of MO_xl_x_*M6_ _ 301875 _ 7548r . 69) ^ ^ fa 



2 x 2 4 



he force with which the string is stretched. Again, a leaden bullet, weigh- 

 ng 2O r , and 6 cm = m -06 distant from the axis would, if fixed to the plate 

 f a whirling-table which makes twelve revolutions in one second (time of 

 otation ith of a second), tend to fly off with a force of 



xfl-oex^ ' 



A x h 



