Theory of Machine
A spring controlled governor is said to be unstable when the controlling force

Increases as the radius of rotation increases
Remains constant for all radii of rotation
Decreases as the radius of rotation increases
Increases as the radius of rotation decreases

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Theory of Machine
The displacement of the reciprocating roller follower, when it has contact with the straight flanks of the tangent cam, is given by (where r₁ = Minimum radius of the cam, r₂ = Radius of the roller follower, and θ = Angle turned by the cam from the beginning of the follower displacement)

(r₁ + r₂) (1 + cosθ)
(r₁ - r₂) (1 - cosθ)
(r₁ + r₂) [(1 - cosθ)/cosθ]
(r₁ - r₂) [(1 - cosθ)/cosθ]

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Theory of Machine
The secondary unbalanced force due to inertia of reciprocating parts in a reciprocating engine is given by (where m = Mass of reciprocating parts, ω = Angular speed of crank, r = Radius of crank, θ = Angle of inclination of crank with the line of stroke, and n = Ratio of the length of connecting rod to radius of crank)

m.ω².r (sin 2θ/n)
m.ω².r sinθ
m.ω².r (cos 2θ/n)
m.ω².r cosθ

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