FRICTION. 



117 



195. The simplest case of pivot friction is that of a vertical shaft of 

 weight W resting with its circular end on a plane horizontal support. 

 If a be the radius of the end of the shaft, the pressure per unit of area 



is W/TTO?, and the pressure on a polar element of area is - rdrdO. 



W ' Ira 



The friction at this element, ^ - - rdrdQ, is directed along the tangent 



to the circle of radius r ; its moment with respect to the centre O of the 



circle is therefore ^-^r z drdO. Hence the whole moment of friction 

 about O is va 



ira' 



This may be regarded as the moment of a force /x W applied at a 

 distance \a from the centre. 



196. Belt-friction, A belt running over two pulleys and stretched so 

 tight as to prevent slipping is a common means of transferring the 

 rotary motion about the axis of one pulley, say A t to the axis of the 

 other pulley B ; A is called the driver, B is the driven pulley. We 

 assume the axes parallel and the rotation counter-clockwise. 



When the pulleys are at rest the tension in CE (Fig. 62) is of course 



Fig. 62. 



equal to the tension in DF. But if the pulley A be set in motion, say 

 by a tangential driving force P acting at a lever-arm /, while the pulley 

 B experiences a resistance Q whose arm is q, the tension in CE will 

 increase to a certain value T lt and the tension in DF will decrease to 

 a value T 2 until the difference 7J 7" 2 is sufficient to overcome the 

 resistance Q. This difference is due to the friction along the surface 

 CGD. If the resistance Q be too great this friction might not be suffi- 

 cient, and slipping of the belt on the driver would occur. 



