The
angular acceleration
a is defined
as the rate of change of the angular velocity. The average angular
acceleration is given by
,

The angular velocity changes when the rotation rate is increasing or
decreasing and when the axis of rotation changes direction.
The angular acceleration is a vector. 
The
angular acceleration is defined as the
rate of change of the angular velocity.
The angular
velocity changes when the rotation rate is
increasing or decreasing and when the
axis of rotation
changes direction.

Problem:
 What is the magnitude of the angular velocity, w,
of the second hand of a clock? What is the direction of
w as you view a clock hanging vertically? What is the
magnitude of the angular acceleration of the second hand?
 Solution:
The second hand of a clock goes through an angular displacement of 2p
in one minute. Its angular speed is w
= 2p/60s
= 0.105/s. The direction of
w is perpendicular to the face of
the clock, pointing into the face of the clock. The average angular
acceleration of the second hand is zero.
Problem:
 What is the angular speed, in radians per second, of
(a) the Earth in its orbit about the Sun, and
(b) the Moon in its orbit about the Earth?
 Solution:
 (a) The earth orbits the sun once every year. The angular speed
of the earth in its orbit about the sun is w =
2p/year
= 2p/(365´24´60´60s)
= 2´10^{7}/s.
 (b) The moon orbits the earth once 27.3 days. The angular speed
of the moon in its orbit about the earth is w=2p/(27.3
days)=2p/(27.3´24´60´60s)
= 2.7´10^{6}/s.
