# Useful Formulae

32 ROTATIONANDBALANCE whirling, gears and pulleys If an object of mass m on a string of length r is swung around in a circle at a velocity of v,then there is a centripetal force F m2r giving acceleration a 2r towards the centre,where is the angular velocity. The centripetal force isequal and opposite to the string tension,which is also treated as a force. Two interlocking gears with t1and t2teeth,and speeds r1and r2 in rpm or any other unit,relate by t1 r1 t2 r2 or equivalently, r1 r2 and r2 r1 The equation also holds true for two belt pulley wheels with diameters t1 and t2 ,and speeds r1 and r2. If two objects with weights w1 and w2 are balanced, as shown opposite, at distances d1 and d2 from a fulcrum, then the torque associated with the two objects must be equal.Torque is the product of force and radial distance. d1w1 d2w2 A longhandled wrench turns a nut more easily than a short handled one because it produces more torque. mv2 r t2 t1 t1 t2 v2 r 33