Begin2.DVI

If
r represents the length and direction of a line drawn to the center of mass of a

body, then

d
r

dt =
v represents the instantaneous velocity of the body and |
v |=v=

∣∣d
r

dt

∣∣

represents the speed of the body. Let mdenote the scalar mass of the body and let

w
denote the vector weight of the body. Here weight is a force given by w
=m
g,

where
g is the acceleration of gravity^6 Denote by m
v the linear momentum of the

body and let F
denote the force acting on a body. Using these symbols Newton’s

second law can be expressed in the form

d

dt

(m
v ) = kF

and if the mass mis a constant, then m

d
v

dt =k

F
or m
a =kF
where kis a propor-

tionality constant and
a =d
v

dt

denotes the acceleration of the body. The value of the

constant kdepends upon the units used to measure distance, time and force.

The following is a set of units for force, mass, distance and time which allow

for the proportionality constant to have the value k= 1. The notation of brackets

around a quantity is used to denote “the dimensions of” the quantity. For example,

the notation, [y] = meters, is read, ”The dimension of yis meters.^7

(fps) System

In the foot (ft), pound (lb), second (sec) system of measurements, one uses

[distance] = ft, [mass ] = lb , [time] = sec, [F orce] = slugs

where 1 slug ·ft/sec^2 = 1 lb force

(cgs) System

In the centimeter (cm), gram (g), second (sec) system of measurements, one uses

[distance] = cm , [mass] = g, [time ] = sec , [F orce] = dynes

where 1 dyne = 1 g·m/sec^2

(mks) System

In the meter (m), kilogram (kg), second (sec) system of measurements, one uses

[distance] = m, [mass] = kg , [time] = sec, [F orce] = N

where 1 N= 1 N ewton = 1 kg ·m/sec^2

(^6) The magnitude of the acceleration of gravity gvaries between 9. 78 m
sec^2 and^9.^82
m
the position of latitude of the body. In this introduction, all particles and bodies are assumed to accelerate in asec^2 and depends upon
gravitational field at the same rate with a value of g=32 secf t 2 or g=980 seccm 2 or g=9. (^8) secm 2.
(^7) Bracket notation for dimensions of a quantity was introduced by J.B.J. Fourier, theorie analytique de la chaleur,
Paris, 1822.