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 (cos 2θ/n)
m.ω².r sinθ
m.ω².r cosθ

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Theory of Machine
The magnitude of velocities of the points on a rigid link is

Inversely proportional to the distance from the points to the instantaneous center and is perpendicular to the line joining the point to the instantaneous center
Directly proportional to the distance from the points to the instantaneous center and is parallel to the line joining the point to the instantaneous center
Inversely proportional to the distance from the points to the instantaneous center and is parallel to the line joining the point to the instantaneous center
Directly proportional to the distance from the points to the instantaneous center and is perpendicular to the line joining the point to the instantaneous center

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