There are two types of balancing:
1. Static balancing
2. Dynamics balancing
In static balancing, we do balancing of unbalanced force in the plane of rotation and in dynamic balancing, we do balancing of the couple generated due to the unbalanced force in different planes.
For balancing a grinding wheel, we need to do balancing in the plane of rotation i.e Static balancing the above figure, if 3 masses are given in a system. Now we need to balance this system. So first we need to draw the force polygon as shown above. Centrifugal force is given by the formula M*r*Angular velocity. So we take all the centrifugal force because of the 3 masses as M1*r1 , M2*r2 and M3*r3 .We didn't take angular velocity as it is the same for all the masses so it will cancel out later. Now make a force polygon taking the direction of the forces from the positive X-axis and finally close the polygon with a vector. This final closing vector will give the magnitude of the centrifugal force for the mass that is required to balance the system. The magnitude will be Mc*rc as shown in the above figure and the direction is given by the vector itself. Now we can place the mass at any convenient radius. So by fixing the radius, we know the mass required to balance the system.
Practically, most industries use vibration analyzer as shown in the above figure. In the figure, the vibration of the electric motor is measured with the analyzer. The analyzer has a magnetic probe which attaches with the system and we then specify the location of the probe and then by running the machine for a while at different speeds we get to know the vibration in terms of peak to peak value or the frequency response also. From that, we can know the location where the balance mass is to be placed and what should be the mass.