---
title: "Block A of mass \\(m_A\\) rests on a horizontal, frictionless tabletop. It is connected by a light string that passes over a pulley to Block B of mass \\(m_B\\), which hangs freely over the edge of the table. The pulley is a solid uniform disk of mass \\(M\\) and radius \\(R\\), and it rotates on a frictionless axle. The rotational inertia of a solid disk is \\(I = \\dfrac{1}{2}MR^2\\). The string does not slip on the pulley. The system is released from rest."
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url: "https://nerd-notes.com/ubq/109541/"
date_modified: "2026-04-01T07:59:30+00:00"
---

# Block A of mass \(m_A\) rests on a horizontal, frictionless tabletop. It is connected by a light string that passes over a pulley to Block B of mass \(m_B\), which hangs freely over the edge of the table. The pulley is a solid uniform disk of mass \(M\) and radius \(R\), and it rotates on a frictionless axle. The rotational inertia of a solid disk is \(I = \dfrac{1}{2}MR^2\). The string does not slip on the pulley. The system is released from rest.

Block A of mass \(m_A\) rests on a horizontal, frictionless tabletop. It is connected by a light string that passes over a pulley to Block B of mass \(m_B\), which hangs freely over the edge of the table. The pulley is a solid uniform disk of mass \(M\) and radius \(R\), and it rotates on a frictionless axle. The rotational inertia of a solid disk is \(I = \dfrac{1}{2}MR^2\). The string does not slip on the pulley. The system is released from rest.

![A schematic showing Block A on a horizontal surface. A string attached to the right side of Block A goes horizontally to a circular pulley mounted at the right edge of the table. The string wraps over the pulley and extends vertically downward to Block B. The pulley has a labeled radius R.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1774412297-Vc2Faj.jpg)

**Part a)** The dots below represent Block A, Block B, and the pulley. On each dot, **draw and label** the forces (not components) that are exerted on that object. Each force must be represented by a distinct arrow starting on, and pointing away from, the dot. *(3 points)*

**Part b)** **Derive** an expression for the magnitude of the acceleration of Block B after the system is released. Express your answer in terms of \(m_A\), \(m_B\), \(M\), \(R\), and fundamental constants, as appropriate. *(4 points)*

**Part c)** If the mass of the pulley \(M\) is made extremely large (so that \(M \gg m_A\) and \(M \gg m_B\)), the acceleration of the blocks approaches zero. **Verify** that your mathematical expression from part (b) predicts this result, and **explain** why this makes physical sense. *(2 points)*

**Part d)** The solid disk pulley is now replaced by a uniform thin hoop of the same mass \(M\) and radius \(R\). The rotational inertia of a hoop is \(I = MR^2\). The system is again released from rest. **Indicate** whether the tension in the horizontal segment of the string (the segment attached to Block A) is greater than, less than, or equal to the tension in that same segment when the solid disk pulley was used. - [ ] Greater than - [ ] Less than - [ ] Equal to **Justify** your answer using physical principles or your derivation from part (b). *(3 points)*


*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/109541/*