Different directed quantities are represented in diagrams by arrows having heads of different shapes. In the case of directed angular quantities, the arrowhead indicates that the torque, angular velocity, angular acceleration or angular momentum is in the clockwise direction about the length of the arrow as axis as seen by an observer looking along the shaft of the arrow toward the head. The arrow-heads used to represent the various directed quantities are as follows:

APPLIED GYRODYNAMICS

CHAPTER I

DEFINITIONS AND PRINCIPLES OF ELEMENTARY
DYNAMICS

§1. Translation and Rotation

1. Linear Motion. Definitions and Units.-Linear displacements are commonly measured in centimeters, meters, kilometers, inches, feet, or miles of various lengths.

1 centimeter = 0.3937 inch

1 meter = 3.2809 feet

1 kilometer = 0.6214 statute mile 1 statute mile = 5280 feet 1 nautical mile = 6080 feet

1 inch = 2.5399 centimeters

1 foot = 0.3048 meter

1 statute mile = 1.6093 kilometers

Linear velocity is time-rate of linear displacement in any given direction. The magnitude of velocity is called speed. Thus, one might say that an automobile is moving with a velocity of 30 miles per hour north but that the automobile is capable of developing a speed of 50 miles per hour. A speed of one nautical mile (6080 ft.) per hour is called a knot. If the linear displacement in every equal time interval t has the constant value x, then the magnitude of the constant linear velocity is

x

V = t   (1)

Linear acceleration is the time-rate of change of linear velocity. There is a linear acceleration whenever either the magnitude or the direction of a linear velocity changes. A body that in every time interval t changes in linear speed from vo to vl while maintain

1