Theory of Machine
For an isochronous Hartnell governor (where r₁ and r₂ = Maximum and minimum radius of rotation of balls respectively, S₁ and S₂ = Maximum and minimum force exerted on the sleeve respectively, and M = Mass on the sleeve)

(m.g - S₁)/(m.g - S₂) = r₂/r₁
S₂/S₁ = r₁/r₂
S₁/S₂ = r₁/r₂
(m.g + S₁)/(m.g + S₂) = r₁/r₂

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Theory of Machine
The static balancing is satisfactory for low speed rotors but with increasing speeds, dynamic balancing becomes necessary. This is because, the

Effects of unbalances are directly proportional to the speed
Unbalanced forces are not dangerous at higher speeds
Effects of unbalances are proportional to the square of the speed
Unbalanced couples are caused only at higher speeds

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