THEORETICAL MECHANICS. 



CHAPTER V. 

 KINETICS OP A PARTICLE. 



I. Impulses ; Impact of Homogeneous Spheres. 



1. Momentum and Impulse. A particle of mass m> moving 

 with the velocity v, is said to have the momentum mv (see Part 

 II., Art. 56). As long as this momentum remains constant, 

 the particle will move in a straight line with constant velocity 

 v (Newton's first law of motion, Part II., Art. 74). Any change 

 occurring in the momentum is ascribed to the action of a force 

 Fon the particle. 



2. If the rate of change of momentum is constant during the 

 time t 1 /, the force F is constant, and is measured by the 

 change of momentum in the unit of time ; that is, 



F(t' t)=mv f mv t (i) 



where v is the velocity at the time /, and v' the velocity at the 

 time t 1 (Newton's second law of motion). As the product 

 F(t' t) of a constant force into the time during which it acts 

 is called the impulse of the force during this time (Part II., Art. 

 61), equation (i) can be expressed in words by saying that 

 the impulse of the force is equal to the change of momentum. 



This proposition is easily seen to hold even for a variable 

 force. For such a force, we have 



PART III I 



