CONSERVATION OF LINEAR MOMENTUM 223 



d?x 

 The right-haud term of equation (69), namely Vm ~T^> can also be 



dx d?x 



modified. Since, by equation (67), we have u = , the value of - 



. du dt dt 



is , so that # x 



By the momentum of a particle, as we have already seen (20), 

 is meant the product of its mass and velocity. The momentum of 

 a particle is therefore a vector of components mu, mv, mw, and mu 

 may be spoken of as the ^-component of the momentum. Each 

 particle of the system will have momentum, and the sum of the 

 ^-components will be C^mu\ the quantity which appears on the 

 right hand of equation (70). 



We may now replace equation (69) by 



where VX denotes the sum of the ^-components of the external 

 forces, and ^mu is the sum of the ^-components of momentum. 



CONSERVATION OF LINEAR MOMENTUM 

 179. When there are no external forces acting, 2/^T = 0, so that 



(2)ra^) = 0. (72) 



d 



Similarly we have (^mv\ =0, (73) 



dt\^ ' 



/ ^r^ \ __ f\ / r 7/i\ 



* 

 These equations express that the quantities 



do not vary with the time. That is to say, the components of the 

 total momentum are constant, so that the total momentum, 



