DYNAMICS OF A RIGID BODY. 309 



1482. A uniform rod is revolving about its middle point, 

 which is fixed, on a smooth horizontal table, when it strikes a 

 smooth inelastic particle at rest, whose mass is to its own as 1 : 6, > 

 and its angular velocity is immediately diminished one ninth; find 



int of impact, and prove that when the particle leaves the 

 rod tlio direction of motion of the ball will make with the rod an ' ^ 

 angle of 45. 



1483. A smooth uniform rod is moving uniformly on a hori- 

 zontal table about one extremity, and impinges upon a particle of 

 ma>s equal to its own, the distance of the point of impact from the 

 fixt-d extremity being to the length of the rod :: 1 : w; prove 

 that the final velocity of the particle will be to its initial ve- 

 locity as 



-lm + 3 : 4m. 



1484. A uniform rod is moving on a horizontal table about 

 one extremity, and driving before it a particle of mass equal to its 

 own, which starts from rest close to the fixed extremity; prove 

 that when the particle lias described a distance r along the rod, its 

 direction of motion will make with the rod an angle 



tan' 1 * 



k being the radius of gyration of the rod about the axis of re- 



>ii. 



1485. A uniform cimilar disc of mass m is capable of nn.t ion 



re in a verticil plai "> U gh {.article of massp 



H plar.-d on it close to the highest point ; prove that the angle 0, 



through which (In- disc will turn before t ho particle begins to sli'le, 



is given liy th'- r,|u:iti"ii 



^ p (m + fy>) coa 0. 



1 1 lifi.rm rod, capable of motion in a vertical plane 



about its mi. 1. 11. point, has attached to its extremities by s- 



jual particl.-.- \\hi.-h hang freely; \\hrn the beam is in e.pii- 



