Angular velocity
Suppose a particle P is moving in a circle as shown below. Let O be the centre and OX be the X-axis. The position of the particle may be described by the angle q. Let the particle move to the position q + dq in a time dt. Assume that the particle keeps changing its position. Thus, we can define a variable called angular velocity which is nothing but the rate of change of angular position.
Units of angular velocity are radsec-1
When the angular velocity remains constant with time, the particle is said to be performing uniform circular motion.
Angular acceleration
If the angular velocity changes with time, then we can define another variable called a (or alpha) which is the symbol for angular acceleration acceleration.If w1 and w2 are the angular velocities at time t = t1 and t = t2 respectively, then average angular acceleration is given by
In the differential form
It is clear from the above stated formula that angular acceleration is the rate of change of angular velocity.
Its unit is radsec-2.Relation between angular variables
Consider the same situation as in the above section.Let the particle move from P to P1 with velocity v in time dt.
Let dq be very small.
