DYHAMIQB Of A i:l<;il> BODY. 315 



gular velocities of the other pairs of rods, and 2a the length of 

 each rod. 



1508. Four equal uniform rods A-B, EC, CD, DE, freely- 

 jointed at B % C t D t are laid on a horizontal table in the form of a 

 square, and a blow is applied at A at right angles to AB from the 

 inside of the square; prove that the initial velocity of A i- 7J 

 times that of E. 



1509. Two equal uniform rods AB, BC, freely jointed at B 

 and moveable about A, are lying on a smooth horizontal table 

 indinrd to each other at an angle a; a blow is applied at at 

 right angles to BC in a direction tending to decrease the angle 

 ABC \ prove that the initial angular velocities of AB, BC are in 

 the ratio 



cos a : 8 3 cos* a ; 



that 0, the least value of the angle ABC during the motion, is 

 given by the equation 



8 (5 - 3 cos 6) (2-cos'a) = (1 -cosa)' (1C - 9 cos 9 a) ; 



and, when a= , that the angular velocities of the rods when in a 



i 



lit line are in the ratio 



- 1 : 3, or 3 : 



). A uniform rod of length 2a rests in a h<ri/ mta! 

 tion with mities on a smooth curve, which is symmetrical 



about a vertical axis; prove mull OM illati 



/Cap cos a (1 + 2 cos* .. 

 \ \3j7 (a p sin* a cos a) j ' 



f > b.-in^ tli tturo and a the angle which th- 



uiakcs with the horizon at either extremity of the rod in tho 



ion .if . .jMilibrium. 



