The one dimensional heat conduction partial difference equation $$\,\,{{\partial T} \over {\partial t}} = {{{\partial ^2}T} \over {\partial {x^2}}}\,\,$$ is

$${i^i}$$, where $$i\, = \,\sqrt { - 1} $$ is given by

A wheel of mass m and radius r is in accelerated rolling motion without slip under a steady axial torque $$T$$. If the coefficient of kinetic friction is $$\mu $$, the friction force from the ground on the wheel is

AB and CD tow uniform and identical bars of mass 10kg each, as shown. The hinges at A and B are frictionless. The assembly is released from rest and motion occurs in the vertical plane. At the instant that the hinge B passes the point B, the angle between the two bars will be