DYNAMICS OF A RIGID BODY. 



6 being the angle tlm-u^h whk-h the two outer rods have turned 

 in a time t, and o> their initial angular velocity. Prove also that 

 the velocity of B(J 



C cos0 



and that the direction of the strain at B or C makes with EC an 

 angle 



tan~ ' (I tail 0\ 



1. Two equal uniform rods AB, EC, freely jointed at B, 

 are in motion on a smooth horizontal table; when is the angle 

 included between them, their angular velocities are o>, ft; prove 

 that 



(."> - 3 cos 0) (o> -I- Q) = c } , 



5w f - 6oO cos 6 + 5Q* = c t ; 

 c,, c, being constants depending on the initial circumstances. 



'2. Three equal uniform inelastic rods, freely jointed at 



tli* it ?s, are laid in a straight line on a smooth horizontal 



table, and the outer are set in motion about the < mis of the middle 



with equal angular velocities, (1) in the same direction, 



opposite directions. Prove that in (1), win n tlu 



make the greatest angle with the . he middle one 



ioed on each side, the common angular velocity of the time 



4 



i (2) that after the impact of the two outer n... 



triangle formed by the three will move \\ith nnifurm velocity 



being the length of eacn rod. 







-'3. A uniform rod of length 2a has attached to one end a 

 particle by a string of length b ; the rod and string are placed in ;i 

 straight line on a smooth horizontal table, and the pa: 



w. :M 



