Do the units match on both sides of the equation?

                                                    1 
    Left-hand side:  omega^2  =  (rad/s)^2  =    ---------
                                                   s^2


                            T         kg*m/s^2            1
    Right-hand side:     ------  =  ------------   =   -------
                          m L         kg * m             s^2


  Yes, the units do match.