The document provides formulae for various mechanical systems including friction, screw threads, clutches, disk brakes, belt drives, bearings, gears, flywheels, rotors, and reciprocating machinery. Key formulae include equations for frictional force, torque required to tighten a nut, axial force in a clutch or brake given a pressure distribution, transmitted power in a belt drive, bearing characteristic number, gear module and ratios, flywheel energy fluctuations given input and output torques, out-of-balance forces and moments in rotors, and primary and secondary out-of-balance forces and moments in reciprocating systems.