Theory of Machine
In a band and block brake, the ratio of tensions on tight side and slack side of the band is (where μ = Coefficient of friction between the blocks and the drum, θ = Semi-angle of each block subtending at the center of drum, and n = Number of blocks)

T₁/T₂ = [(1 - μ tanθ)/(1 + μ tanθ)]n
T₁/T₂ = [(1 + μ tanθ)/(1 - μ tanθ)]n
T₁/T₂ = (μ θ)n
T₁/T₂ = μ. θ. n

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Theory of Machine
Two heavy rotating masses are connected by shafts of lengths l₁, l₂ and l₃ and the corresponding diameters are d₁, d₂ and d₃. This system is reduced to a torsionally equivalent system having uniform diameter d = d₁ of the shaft. The equivalent length of the shaft is

l₁ + l₂ + l₃
l = l₁ + l₂.(d₁/d₂)⁴ + l₃.(d₁/d₃)⁴
(l₁ + l₂ + l₃)/3
l = l₁ + l₂.(d₁/d₂)³ + l₂.(d₁/d₃)³

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