9 2 



KINEMATICS. 



since #=0, jj/=o for tO. Eliminating t, we find the equation! 

 of the path of the projectile : 



,0)86 CX 



V n COS 6 



(II) 



The curve has a vertical asymptote x=- ; for this value 

 of x, /=oo . 



171. Uniform Circular Motion. Let a point P (Fig. 43) describe 

 a circle of radius a with constant angular velocity co. Its linear 



Fig. 43. 



velocity v = wa is of constant magnitude, but varies in direction. 

 By the formulae (i), (2) of Art. 159, the tangential acceleration 

 j t = o, while the normal acceleration j n = v 2 '/a = aPa represents 

 the total acceleration. Hence, in uniform circular motion, the 

 acceleration is 



j=* = tfa t (12) 



and is always directed toward the centre O of the circle. 



This appears also by constructing the hodograph of the 

 motion, which is evidently a circle of radius v (Fig. 43). As 

 the acceleration of P is represented by the velocity of the point 

 P' of the hodograph (see Art. 156), we have only to determine 

 this velocity. Let T be the so-called period, or periodic time, 

 i.e. the time in which the point P makes a whole revolution, 



