Theory of Machine
A torsional system with discs of moment of inertia I₁ and I₂ as shown in the below figure, is gear driven such that the ratio of speed of shaft B to shaft A is 'G'. Neglecting the inertia of gears, the equivalent inertia of disc on shaft B at the speed of shaft A is equal to

G.I₂
I₂/G²
G².I₂
I₂/G

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Theory of Machine
The frictional torque transmitted in a truncated conical pivot bearing, considering uniform pressure, is

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

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Theory of Machine
The velocity of piston in a reciprocating steam engine is given by (where ω = Angular velocity of crank, r = Radius of crank pin circle, θ = Angle turned by crank from inner dead center, and n = Ratio of length of connecting rod to the radius of crank)

ωr [sin θ + (sin 2θ/n)]
ω²r [sin θ + (sin 2θ/n)]
ωr [cos θ + (cos 2θ/n)]
ω²r [cos θ + (cos 2θ/n)]

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