C E N 



Ex. 2. Angular velocity in a conic section ,' do. in ti circle at the same 

 distance :: (i L)i : (SP)$. 



Ex. 3. Angular velocity in ellipse : mean angular velocity I : , 



1 

 * ACTCB' 



Ex. 4. Angular velocity at mean distance I mean angular velocity '.". 

 CB I CA. 



Let u, be the angular velocity in any curve, then the rate at which it 

 decreases, or 



V 7/2 ])* 



a vanes as * . 



py\ 



Ex. 1. In a parabola, the decrement of the angular velocity is a maxi- 

 mum, when y ^- (a = % L. R.) 



Ex. 2. In the ellipse, the decrement is a max. when 3*/s 7 ay -J" 



4 6* = o. 



5. Of the paracentric velocity in any curve. 



V ?/2 2 



Par. velocity varies as . 



py 



Ex. 1. In parabola, par. velocity is a maximum whcny = 1 a. 

 Ex. 2. In ellipse, y = | L. 



6. Of the centrifugal force of bodies revolving in trajectories. 

 Let a twice area described in 1", then 



Centrifugal force 5-. 



And centripetal force .* centrifugal :: 2SPs : SY2x PV, or :: 

 y 3 - dy 



Ex. 1. In an ellipse (force in the centre), centripetal ,* centrifugal 

 force : : C P* : A C 8 x C B 2 . 



Ex. 2. In conic sections (force in the focus) centrifugal force = 

 and centripetal : centrifugal force 1 1 S P I | L. 



7. Of the periodic times of bodies revolving in trajectories. 



51 



