Obtain and expression for thework done by a torque.

1.	Obtain and expression for thework done by a torque.
Answer» Solution : 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`

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