An Atwood machine consists of two blocks of masses \(m_1\) and \(m_2\), with \(m_1 > m_2\), connected by a light, inextensible string that passes over a pulley of radius \(R\) and rotational inertia \(I\). The string does not slip relative to the pulley, and a constant frictional torque of magnitude \(\tau_f\) opposes the rotation of the pulley about its central axle. The system is released from rest and accelerates. Which of the following expressions is equal to the difference in the string tensions, \(T_1 - T_2\), where \(T_1\) is the tension in the segment supporting mass \(m_1\) and \(T_2\) is the tension in the segment supporting mass \(m_2\)?