MOTION AND FORCE 19 
mass of matter weighing g pounds, so that if W is the weight of a body 
in pounds, its mass is M= W 
ro 
‘e 26. Momentum.—The quantity of motion or the momentum of a’ 
moving body is measured by the product of its mass and velocity. 
~ Momentum = Mv = Wo. 
27. Newton’s First Law of Motion.—Zvery body continues in its 
state of rest or of uniform motion in a straight line, except in so far as it 
may be compelled by force to change that state. 
28. Newton’s Second Law of Motion.— Late of change of momentum 
ts proportional to the impressed force, and takes place in the direction of 
the straight line in which the force acts. 
Rate of change of momentum is equal to mass multiplied by rate of 
change of velocity or acceleration. Hence if P denotes the impressed 
force, M the mass of the body, and f the acceleration, Pa Mf. If the 
unit of force be such as will give unit mass unit acceleration, then P= Mf. 
Using engineer’s units, P= v f or = =f : 
29. Impulse.—If a constant force P acts on a mass M for ¢ seconds, 
then, since P= M/, it follows that Pt = M/t = M», where v is the change in 
the velocity of the body in the time ¢ due to the action of the force P. 
_ The product P¢ is called the impulse of the force P. The impulse of 
a force is therefore equal to the change in the momentum which the 
_ force produces in the body on which it acts. 
If the force is not constant the above equations are only true if ¢ is 
‘indefinitely small, or if P is the average value of the force during the 
time te 
__ The equation P¢ = Mv also shows that equal forces acting on different 
masses will in the same time produce in these masses equal amounts of 
momentum. For example, when a projectile is fired from a gun, the 
forward momentum of the projectile is equal to the backward momentum 
of the gun. 
30. Newton’s Third Law of Motion.—70 every action there is always 
an équal and opposite reaction. For example, a body is attracted to the 
~ earth by the force of gravity, but it is equally true that the earth is 
attracted to the body by an equal force. Again, a body resting on a 
table exerts a pressure on the table, but the table exerts an equal pressure 
on the body. 
31. Centrifugal Force.—When a point moves in a circle of radius r 
_ feet with a uniform velocity v feet per second, or an angular velocity of 
w radians per second, it has been shown (Art. 21) that the point has a 
radial acceleration f equal to v*/r or w*r. If the point be replaced by a 
small body of weight w lbs., then a radial force F must be applied to the 
body to constrain it to move in the circle, the magnitude of F, in Ibs., being 
eee 2" XS fheve dcactibed, the force F is called the deviating 
RS ae | ‘ 
force or the centripetal force. The body in moving in the circle will 
evidently exert an equal radial force F acting outwards from the centre, 
‘and this force is called the centrifugal force. Of these two forces, the centri- 
petal and the centrifugal, one may be said to be the reaction of the other. 
