290 APPLIED MECHANICS ‘: 
second, and the acceleration / feet per second per second. Let the scales 
be—space, 1 inch to 7 feet; velocity, 1 inch to m feet per second ; accel- 
eration, 1 inch to m feet per second per second; and time, 1 inch to 
q seconds. Also let OP=p inches, and OP, =p, inches. 
Then from the simple geometry cf the figure 
ds ot v is qv 
ong moe? Or eT mp : (1) 
bv bt of. yig ¥ 
also mye eee Maia oD 
but a= (approximately)... (3), and =f (approximately)... (4). 
Therefore from (1) and (3) ae as and from (2) and (4) £ a... Hence | 
1 
if q, P; Py and, say, m are eae 4 and » can be found, or if 7, m, n, and g 
are given, p and p, can be found. 
255. Angular Motion Diagrams.—In the preceding Articles of this 
chapter only linear distance or displacement, linear velocity, and linear 
acceleration have been referred to, but all that has been said about the 
relations between these also applies to the relations between angular dis- 
placement, angular velocity, and angular acceleration, Angular displace- 
ment, measured in radians, angular velocity in radians per second, and 
angular acceleration in radians per second per second, may be plotted on 
a straight time base, and angular velocity, angular acceleration, and time 
may be plotted on a straight base representing angular displacements, 
exactly as for linear motion. 
256. Examples.—(1) The tractive force on a car weighing 10 tons i is 
P lbs., and there is a uniform resistance R Ibs., so that the unbalanced 
effort F i is P—R lbs. Values of F at intervals of 2 seconds are given in 
the second column of the table below. The car is at rest when the time 
tis 0. It is required to determine the acceleration / of the speed of the — 
car in feet per second per second, the velocity v of the car in feet per — 
second, and the distance s travelled from the starting point in feet at 
each of the given times ¢. 
Accelera-| Mean | Increase Velocity Mean _ | Distance | Distance 
tion (/). } Accelera- in 
halanied Velocity | moved 
() Effort Highs | F os ae tion Velocity Feet r | during during . 
during | during | “Qed pe Interval. | Intervat. | Start (s).! 
| _ ice | Interval. | Interval. / Feet. — 
| 4 
oh ean 0-877 0-348 | 1-696 | °. 0-348 | 1:70 | P29 
2 | 570 | o-si9 | 2% 1-696 | 9. 
0-775 | 1-550 | 1696 | 9-471 ~ 
4 508 0°730 3 " 3°246 4 7:82 4 
; 0-664 | 1-328 | 3 3-910 rie 
6 | 416 | 0-598 | 0-664 | 1° 4-574 | 3. be: 
0-522 | 1-044 | * 5-096 | 1019 | dager 
s | 310 | 0-446 | % Ro hag eee bees 7 
0-433 | 0-366 | 5 6-051 | 12 
10 | 292 | 0-499 | 0°33 | 0° 6-434 | 8 re. 
0-393 | o-786 | & 6877 | 13°75 | go. 
12° | 255 | 0-367 | 2 7-270 | 8 
0-370 | o-740 | o 7640 | 15:28 | pric 
14 | 260 | 0-374 | 2 s-o10 | 2 ; 3 
‘B74 | 0-402 | 0-904 | S010 | gaia | 16-82 | 20. 
16 | 300 | o-431 | % es) SBT ; 
0-438 | 0-876 | 8 9-252 | 18°50 | B60 
18 | 309 | Ot | 0-459 | 0-918 | 42.09 | 10-149 | 20°30 | 70r 4p | 
20 | 330 | 0-474 12140 © 
