GENERAL PRINCIPLES 



This formula expresses the well known law of the fall of bodies, 

 the spaces covered being proportional to the squares of the time 

 taken to traverse them. 



So far we have been considering motion in a straight line. 

 Similar considerations apply to motion along a curved path. 



The most common example of curvilinear motion is that in 

 which the path is the circumference of a circle. The elements 

 of many machines, such as the arms of a windmill, waterwheels, 

 the flywheels of engines, and the like, have this circular move- 

 ment which is generally uniform. 



The speed of the moving body M (fig. 1), in a uni- 

 form circular motion, is the arc described in a 

 second. If it described the whole circumference 



2-r:r in t seconds, the speed would be v = 





If in 



Fw. 1. 



a second it goes from M to M ' the arc MM ' will be 

 tor = v. The angle CD (omega) is called the angular 

 speed of the moving body. From the two ex- 



2nr 



pressions, --- and tor, for v we deduce 



In the case of high velocity, we consider the number of revolu- 

 tions per second, n times 2nr. 



To define the unit of speed assume a circle with a radius equal 

 to 1, shown dotted in fig. 1. If the radius is taken as the unit 

 of arc, it is contained 2n times in the circumference ; the arc 

 equal to the radius is called a radian and corresponds to an angle 

 of about 57 18' because 180 (2 right angles) corresponds to TT 

 radians. 



180 180 



3-1416 



5718'. 



Hence, given an angular speed 

 co (in degrees) it would be ex- 

 pressed in radians by the formula 

 180 _ 



" 180 



i 



co = 



'>^ 



