Here are some examples of inertia for a 2m wide roll of several products.
OPP Paper Aluminum Steel
100mm core (kg*m^2) 1.0 1.0 1.0 1.0
500mm roll (kg*m^2) 11.2 7.2 31.0 94.9
Density (kg/m^3) 946 600 2700 8000
As the diameter changes, the RPM decreases. The torque required for accelerating the roll is Moment of Inertia * Angular Acceleration. The Inertia of the roll increases as diameter ^4, but the acceleration decreases with diameter. Therefore torque increases as diameter^3, but is shaped like a quadratic. Generally the torque required is greatest at the maximum diameter, near minimum at the core and its minimum value is just a bit larger than the core diameter.
For unwinds (or winders), there is a specific diameter where the inertia compensation exactly matches the tension torque during acceleration (deceleration). At this diameter the unwind brake (winder drive) produces no torque, but tension is correct. Under this circumstance we often hear the drive train gears and couplings chattering.
For unwinds, the most thermal stress is put on the motor when decelerating with a large roll. That is because tension and deceleration both act in the same direction. This occurs while stopping to patch a web defect just after accelerating with a large roll.
Moment of Inertia is the biggest factor in tuning the speed regulator. If an unwind or winder drive is used for threading the line, the tuning should be optimized for the diameter at which the line is most often threaded. For unwinds that is a large diameter. For winders that is core diameter.