Theory of Machine
In a Hartnell governor, the lift of the sleeve is given by (where r₁ and r₂ = Max. and min. radii of rotation, x = Length of ball arm of the lever, and y = Length of sleeve arm of the lever)

(r₁ - r₂) (y/x)
(r₁ - r₂) (x/y)
(r₁ + r₂) (x/y)
(r₁ + r₂) (y/x)

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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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Theory of Machine
Crowning on pulleys helps

In increasing velocity ratio
Increase belt and pulley life
For automatic adjustment of belt position so that belt runs centrally
In decreasing the slip of the belt

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