2i6.] PLANE MOTION. 



/=0, and AOP Q = Q , then the arc P P=s described in the 

 time/ is j = /(0 -0); hence v=ds/dt= -IdO/dt, and dfr/dT/ 

 = Id 2 6/dt*, the negative sign indicating that diminishes as 

 j and / increase. 



Resolving the acceleration of gravity, g> into its normal and 

 tangential components gcosO, -sin#, and considering that the 

 former is without effect owing to the condition that the point 

 is constrained to move in a circle, we obtain the equation of 

 motion in the form dv/dt =g sin 0, or 



(32) 



216. The first integration is readily performed by multiplying 

 the equation by dQjdt which makes the left-hand member an 

 exact derivative, , 



hence integrating, we obtain 



or considering that v=ldQldt, 



To determine the constant C, the initial velocity ^ at the 

 time t=o must be given. We then have J^ 2 

 hence 



cos e=g-lcvs + /cos (33) 



The right-hand member can readily be interpreted geometri- 

 cally ; v^/2g is the height by falling through which the point 

 would acquire the initial velocity V Q (see Art. 113); /cos# 



