Applied Mechanics and Graphic Statics
‘ω’ rad/sec is the angular velocity of a crank whose radius is ‘r’. If it makes θ° with inner dead centre and obliquity of the connecting rod ‘l’ is ‘ϕ’, the velocity v of the piston, is given by the equation

ω² (l sin ϕ + r cos φ tan θ)
ω (l sin ϕ + r cos ϕ tan θ)
ω² (l cos ϕ + r sin ϕ tan θ)
ω² (l sin ϕ - r cos θ tan ϕ)

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Applied Mechanics and Graphic Statics
A square hole is punched out of a circular lamina, the diagonal of the square being the radius of the circle. If ‘r’ is the radius of the circle, the C.G. of the remainder from the corner of the square on the circumference will be

[r (π + 0.25)]/(π + 0.5)
[r (π - 0.25)]/(π - 0.5)
[r (π + 0.25)]/(π - 0.5)
[r (π - 0.5)]/(π + 0.25)

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