In the diagram v is the tangential velocity of the object. a is the centripetal (acting towards the center of the circle) acceleration and Fis the centripetal force. r is the radius of the circle and m is mass of the object.
Consider that there are a number of particles forming a system, such that, when an external force is applied, the complete system moves as on. Now, if we are able to replace all these particles by just one particle. And, this new particle is placed in such a manner and has such a mass, that when acted on by an external force, it moves exactly in the same manner as the system it replaced. Then, we have found the center of mass of the system. (This sounds more complex than it is. So don't worry! read on)
Let us now consider two particles. Let them have masses m_{1} and m_{2}. Let r_{1}(t) and r_{2}(t) be the position vectors of the two particles at the instant of time t. (Note: On a web page it is difficult to use the usual vector notation. So I will use bold fonts to depict vectors). The position vector R_{c.m.}(t), giving the center of mass of this system is given by the formula.
R_{c.m.}(t) = {m_{1}r_{1}(t) + m_{2}r_{2}(t)} / (m_{1} + m_{2})
from the above it is obvious that for a two particle system the center of mass always lies between the two particles. It also lies on the line joining the two particles.
R_{c.m.}(t) = {m_{1}r_{1}(t) + m_{2}r_{2}(t) +  m_{n} r_{n}(t)} / (m_{1} + m_{2 }+  m_{n})
The position of the center of mass of a rigid body is a fixed point. This point may or may not lie in the body. Where is lies depends upon the shape of the body. For example of we take the case of a ring. The center of mass will lie at its geometrical center. Obviously this point does not lie in the ring.
Body  Center of mass  
Rod 
Mid point of rod 

Ring 
Center of ring 

Sphere 
Center of sphere 
Average angular velocity = Angular displacement / time interval
So if ω is the average angular velocity, θ the angular displacement and t the time interval. We can say
So we can write the instantaneous angular velocity as dθ /dt
Linear velocity = Radius of the circular path x Angular velocity
Average angular acceleration = Change in angular acceleration / Time interval
Linear acceleration = Radius of the circular path x Angular acceleration