Circular motion:
Angular displacement: When a particle is in circular motion about an axis or centre, the angle described by the radius about the axis or centre is called angular displacement.
A particle rotates in a circular path of radius r about the centre O.
The particle moves from A to B through the circumference of the circle.
The angular displacement of the particle is 
= 
= 
SI unit of angular displacement is radian. 
radian = 
.
Dimension of angular displacement 
or dimensionless.
Angular speed: The angular displacement per unit time is called angular speed.
If 
is the angular displacement for time 
t then angular speed is 
 [where  represents the small change.]
SI unit of angular speed is radian/second or 
.
Dimension of angular speed is 
.
Another unit of angular speed is revolution per minute (rpm) = 1rpm = 
= 
.
Time period: The time taken by the particle to complete one rotation is called time period.
Frequency: The number of full rotation completed by the particle in one second is called frequency.
So, Frequency = 
.
Relation between angular speed and time period: Angular speed = 
.
Relation between linear speed and angular speed: A particle rotates in a circular path of radius r about the centre O. The particle moves from A to B through the circumference of the circle.
The angular displacement of the particle is  for time t. Then angular speed is .
If the distance travelled by the particle is arc AB = 
then  = 
.
So, Â = 
 = 
 [where linear speed v = 
]
v = 
.
Angular acceleration: The change of angular velocity per unit time is called angular acceleration.
If 
is the change of angular velocity for time 
 then angular acceleration is 
.
SI unit of angular acceleration is 
.
Dimension of angular acceleration is 
.
Relation between linear acceleration and angular acceleration: A particle rotates in a circular path of radius r about the centre O. The particle moves from A to B through the circumference of the circle for time .
The change of angular velocity of the particle from A to B is . Then angular acceleration is .
If 
is the change in linear velocity of the particle from A to B then linear acceleration 
[as v = r  so, = r where r is constant].
So, a = r
.
Video explanation of this post.