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title: "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\\)?"
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url: "https://nerd-notes.com/ubq/124398/"
date_modified: "2026-09-28T14:05:11+00:00"
---

# 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 \(m_2\)?

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 \(m_2\)?

![A circular disk of radius \(R\) represents a pulley centered on a fixed horizontal axle indicated by a small filled circle at its center. A curved arrow labeled \(\tau_f\) is positioned near the axle pointing counterclockwise to indicate frictional torque opposing clockwise rotation. A continuous line representing a string hangs vertically from the left and right rims of the disk. Suspended from the left vertical segment is a rectangular block labeled \(m_2\). Suspended from the right vertical segment is a larger rectangular block labeled \(m_1\), hanging lower than block \(m_2\). A straight radial dashed line extends from the center of the disk to its top edge, labeled \(R\). A straight downward vertical arrow labeled \(g\) is positioned to the far right of the pulley. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604311-dUYSda.jpg)

- **A.** \(\dfrac{I(m_1 - m_2)g}{I + (m_1 + m_2)R^2}\)
- **B.** \(\dfrac{I(m_1 - m_2)g - (m_1 + m_2)R\tau_f}{I + (m_1 + m_2)R^2}\)
- **C.** \(\dfrac{I(m_1 - m_2)g + (m_1 + m_2)R\tau_f}{I + (m_1 + m_2)R^2}\)
- **D.** \(\dfrac{I(m_1 - m_2)g + \left(\dfrac{I}{R} + (m_1 + m_2)R\right)\tau_f}{I + (m_1 + m_2)R^2}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124398/*