370-] 



CONTINUOUS MOTION OF FREE BODY. 



207 



pulsive reaction P of the fixed point ; hence the resultant impulse 

 =F-\-P, the resultant couple = Fx^ + Px. 



As the point P of the body is reduced to rest by the impact, we 

 have only to express the velocity of 

 P and equate it to zero. This gives 

 the condition 



F+P 



M 





Mf 



x = o, 



whence 

 p _ 



u 



since xxi = g 2 . This becomes = F 

 for x = o and for x = Xi. 



Show that there are two points of 

 maximum impact on GO at equal 

 distances from / on opposite sides, and that the maximum impulse is 



Fi 54 



(7) A free rigid body turns with angular velocity o> about a centroidal 

 principal axis 1 when one of its points P, situated at the distance x from 

 1 in the centroidal plane perpendicular to 1, strikes a fixed obstacle. 

 Determine the impulse on this obstacle, and show that it is greatest 

 when x = q, where q is the radius of inertia for I. * 



(8) In Ex. (6), determine the initial motion of the body after striking 

 the fixed obstacle. 



2. CONTINUOUS MOTION. 



370. In the preceding articles (357-367) it has been shown 

 how to determine a system of impulses capable of producing 

 any given instantaneous state of motion of a free rigid body. 

 Any change in the state of motion can be regarded as due to 

 a system of forces ; and by reducing the effective forces of the 

 particles, in a similar way as has been done for the momenta, 

 this system of forces can be determined. This geometrical 

 study of the continuous motion produced by forces is here 

 omitted, as it would require a more complete exposition of the 

 theory of acceleration than has been given in the first part of 

 the present work. 



