# Maths

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The distance from TDC (top dead centre) for the pin is given by x when the crank is
at angle . Hence :
i) Give an equation for x in terms of the other variables (r, L and ).

ii) If the crank rod is rotating at a constant value of ω calculate the speed of the
piston
i.e. calculate
dt
dx
in terms of ω, r,  and L
iii) Hence calculate the x value when the speed of the piston is at a maximum.

iv) If L is 1 metre, r is 0.25 metres and the crank is rotating at 5,000 rpm
calculate the maximum velocity of the piston in m/s.

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