S9 .] MOMENTUM. 35 



58. Momentum, being by definition (Art. 56) the product of 

 mass and velocity, has for its dimensions (see Kinematics, Art. 92) 



MV = MLT~ 1 . 



The unit of momentum is the momentum of the unit of mass 

 having the unit of velocity. 



Thus in the C.G.S. system the unit of momentum is the 

 momentum of a particle of I gramme moving with a velocity of 

 i cm. per second. There is no generally accepted name for this 

 unit, although the name bole was proposed by the Committee of 

 the British Association. 



In the F.P.S. system, the unit is the momentum of a particle 

 of one pound mass moving with a velocity of I ft. per 

 second. 



To find the relations between these two units, let there be x 

 C.G.S. units in the F.P.S. unit ; then 



gm. cm. Ib. ft. . 



x 5 = i ; 



sec. sec. 



Ib. ft. 

 hence . 



gm. cm. 

 or, by Art. 3 and Kinematics, Art. 14, 



^=453.59x30.48=13825.3; 



i.e. i F.P.S. unit of 'momentum =13825.3 C.G.S. units, and 

 i C.G.S. unit =0.000072331 F.P.S. units. 



59. Exercises. 



(1) What is the momentum of a cannon-ball weighing 200 Ibs. when 

 moving with a velocity of 1500 ft. per second? 



(2) With what velocity must a railroad-truck weighing 3 tons move 

 to have the same momentum as the cannon-ball in Ex. (i) ? 



(3) Determine the momentum of a one- ton ram after falling through 

 20 feet. 



