---
title: "A uniform solid disk of mass \\(M\\) and radius \\(R\\) is mounted on a horizontal, frictionless axle. The axle passes through point \\(P\\), which is located a horizontal distance \\(d\\) from the geometric center \\(C\\) of the disk. The disk is initially held at rest in an orientation such that \\(C\\) is directly to the right of \\(P\\), making the line connecting \\(P\\) and \\(C\\) horizontal.  A light string is wrapped around the circumference of the disk, and the string does not slip. Block 1 of mass \\(m_1\\) hangs from the left side of the disk, and Block 2 of mass \\(m_2\\) hangs from the right side. The system is initially held at rest by a locking pin at point \\(P\\) that prevents the disk from rotating."
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url: "https://nerd-notes.com/ubq/110575/"
date_modified: "2026-04-08T04:14:05+00:00"
---

# A uniform solid disk of mass \(M\) and radius \(R\) is mounted on a horizontal, frictionless axle. The axle passes through point \(P\), which is located a horizontal distance \(d\) from the geometric center \(C\) of the disk. The disk is initially held at rest in an orientation such that \(C\) is directly to the right of \(P\), making the line connecting \(P\) and \(C\) horizontal.

A light string is wrapped around the circumference of the disk, and the string does not slip. Block 1 of mass \(m_1\) hangs from the left side of the disk, and Block 2 of mass \(m_2\) hangs from the right side. The system is initially held at rest by a locking pin at point \(P\) that prevents the disk from rotating.

A uniform solid disk of mass \(M\) and radius \(R\) is mounted on a horizontal, frictionless axle. The axle passes through point \(P\), which is located a horizontal distance \(d\) from the geometric center \(C\) of the disk. The disk is initially held at rest in an orientation such that \(C\) is directly to the right of \(P\), making the line connecting \(P\) and \(C\) horizontal.

A light string is wrapped around the circumference of the disk, and the string does not slip. Block 1 of mass \(m_1\) hangs from the left side of the disk, and Block 2 of mass \(m_2\) hangs from the right side. The system is initially held at rest by a locking pin at point \(P\) that prevents the disk from rotating.

![A circle representing the uniform solid disk. A small dot labeled 'C' is at the exact center of the circle. Another small dot labeled 'P' is horizontally to the left of 'C' by a distance labeled 'd'. A dashed horizontal line passes through P and C. The radius of the disk is marked as 'R'. A string wraps over the top half of the circle and hangs vertically downward from both the far left and far right edges. A square block labeled 'm_1' is attached to the bottom of the left string. A square block labeled 'm_2' is attached to the bottom of the right string.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1775539153-Hb5wir.jpg)

**Part a)** On the diagram of the disk below, **draw** and **label** the forces (not components) that exert a nonzero torque on the disk about the axle at point \(P\) when the system is held at rest. Each force must be represented by a distinct arrow starting on, and pointing away from, the point at which the force is exerted on the disk. *(2 points)*

**Part b)** The locking pin is removed, but the system is observed to remain in static equilibrium. **Derive** an expression for the mass \(m_2\) required for the system to remain in static equilibrium. Express your answer in terms of \(m_1\), \(M\), \(R\), \(d\), and fundamental constants. *(3 points)*

**Part c)** The blocks and string are now removed from the disk. The bare disk is held in the same initial orientation, with its center \(C\) located a horizontal distance \(d\) directly to the right of the axle at \(P\). *(3 points)*

**Part d)** As the bare disk rotates from its initial horizontal orientation until point \(C\) is directly below point \(P\), **indicate** whether the magnitude of the angular acceleration of the disk increases, decreases, or stays the same. - [ ] Increases - [ ] Decreases - [ ] Stays the same **Justify** your answer. *(3 points)*


*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/110575/*