Obtain and expression for the work done by a torque.

Explanation

Let `F_1` be the force on `P_1` at a distance `r_1` from O. The are distance `P_1P_2=ds_1` i.e. `ds_1=r_1dtheta`
Work done by the force `dW_1=F_1ds_1cosphi_1`
i.e `dW_1=F_1(r_1dtheta)sinprop_1`
`:'phi_1+prop=90^(@)`
`cosphi_1=cos(90-prop)=sinprop`
i.e `dW_1=tau_1dtheta. :.tau_1=F_1r_1sinprop_1`
If there are more than one force acting at different points on the body, then the total work done by the torque `dW=dW_1+dW_2+dW_3+.......dW_n`
i.e., `dQ=(tau_1+tau_2+...+tau_n)dtheta`
i.e `dW=taudtheta` where `tau=sumtau_i`