Page 127 - Schaum's Outline of Theory and Problems of Applied Physics

CHAPTER 10

Rotational Motion

ANGULARMEASURE

◦
In everyday life, angles are measured in degrees, where 360 equals a full turn. An often-used unit in technology
is the radian (rad). If a circle is drawn whose center is at the vertex of a particular angle (Fig. 10-1), the angle θ
(Greek letter theta) in radians is equal to the ratio between the arc s cut by the angle and the radius r of the circle:
s
θ =
r
arc length
Angle in radians =
radius

Fig. 10-1

Because the arc length of a circle of radius r is its circumference 2πr, there are 2π rad in a complete revolution
(rev). Hence
1rev = 360 = 2π rad
◦
and so
◦
◦
1 = (2π/360) rad = 0.01745 rad 1 rad = (360/2π) = 57.30 ◦
ANGULARVELOCITY
The angular velocity of a body describes how fast it is turning about an axis. If a body turns through the angle θ
in the time t, its angular velocity ω (Greek letter omega)is
θ
ω =
t
angular displacement
Angular velocity =
time
112