Work done by a torque

Abstract It is well known that the work done by a torque, τ , during a small angular displacement <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>d</mml:mi> <mml:mi>θ</mml:mi> </mml:mrow> </mml:math> is given by <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>τ</mml:mi> <mml:mi>d</mml:mi> <mml:mi>θ</mml:mi> </mml:mrow> </mml:math> . The same relation applies if a ball is rolling down an incline, even if the torque arises from a static friction force. However, it is usually assumed that the work done by a static friction force is zero.