MOMENT OF INERTIA
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The more the mass is far from the axis → the greater the moment of inertia
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The more the mass is close to the axis → the lower it is
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With equal total mass, the distribution changes everything
In watchmaking, the Moment of inertia mainly concerns the Balance. The Moment of inertia of the Balance is calculated using the following formula:
l = Moment of inertia of the Balance (kg × m²)
m= Mass of the Balance (kg)
r= radius of gyration of the Balance (m)
The Frequency of the Regulating organ (and therefore its Period) directly depends on the Moment of inertia of the Balance and the Stiffness (spring rate) of the Hairspring (balance spring) according to the following relationship:
T = Period (s)
l = Moment of inertia of the balance around its axis (kg×m²)
C = Elastic moment (torque) (stiffness) of the hairspring (balance spring) (N×m/rad)
Certain constructions make it possible to modify the moment of inertia of the balance in order to carry out its poising and its regulation / adjustment (Figure 1).
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