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
angular displacement  to the time t, in which this displacement was

passed, is the constant value and is called the angular velocity of the
uniform motion (compare with definition of linear .velocity)

 
 
t . (2.1)
As angular displacement is a vector, accordingly angular velocity
is a vector as well, which coincides with the vector of angular

displacement (fig 2.1). In scalar form

 
t (2.2)

and is expressed in radians per second ( rad ).
s
The rotational period T of rigid body is the time that is
needed to complete one revolution around the axis of rotation. So if one

revolution corresponds to the angle 2 radian, then
2 
 
T (2.3)

Frequency  of rotation is the number of complete revolution
occurred per unit of time and is inversely proportional to rotation
period
1
 (2.4)
T

therefore
  2     . (2.5)
For non-uniformly rotational motion instantaneous angular
velocity is the first derivative of angular displacement with respect

to time (similar definition of linear instantaneous velocity )

 d
 
dt (2.6)
or in scalar form

d
  . (2.7)
dt
If for any, but equal intervals of time t , modulus of angular
velocity changes in uniform manner , increase or decrease on the same

value  , this motion is called uniformly accelerated rotational
motion. For such motion the new term angular acceleration is

introduced

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