Theory of Machine
When the crank is at the outer dead centre, in a reciprocating steam engine, then the acceleration of the piston will be

ω² r {(n - 1)/n}
ω² r {n/(n - 1)}
ω² r {(n + 1)/n}
ω² r {n/(n + 1)}

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

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Theory of Machine
The frictional torque transmitted in a flat collar bearing, considering uniform wear, is (where r₁ and r₂ = External and internal radii of collar respectively)

(2/3) μ W (r₁ + r₂)
(1/2) μ W (r₁ + r₂)
(2/3) μ W [(r₁³ - r₂³)/(r₁² - r₂²)]
(1/2) μ W [(r₁³ - r₂³)/(r₁² - r₂²)]

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