---
title: "A system consists of two small disks, of masses \\( m \\) and \\( 2m \\), attached to a rod of negligible mass of length \\( 3l \\) as shown above. The rod is free to turn about a vertical axis through point \\( P \\). The two disks rest on a rough horizontal surface; the coefficient of friction between the disks and the surface is \\( \\mu \\). At time \\( t = 0 \\), the rod has an initial counterclockwise angular velocity \\( \\omega_0 \\) about \\( P \\). The system is gradually brought to rest by friction. Develop expressions for the following quantities in terms of \\( \\mu \\), \\( m \\), \\( l \\), \\( g \\), and \\( \\omega_0 \\)."
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url: "https://nerd-notes.com/ubq/79938/"
date_modified: "2025-03-07T06:29:57+00:00"
---

# A system consists of two small disks, of masses \( m \) and \( 2m \), attached to a rod of negligible mass of length \( 3l \) as shown above. The rod is free to turn about a vertical axis through point \( P \). The two disks rest on a rough horizontal surface; the coefficient of friction between the disks and the surface is \( \mu \). At time \( t = 0 \), the rod has an initial counterclockwise angular velocity \( \omega_0 \) about \( P \). The system is gradually brought to rest by friction. Develop expressions for the following quantities in terms of \( \mu \), \( m \), \( l \), \( g \), and \( \omega_0 \).

A system consists of two small disks, of masses \( m \) and \( 2m \), attached to a rod of negligible mass of length \( 3l \) as shown above. The rod is free to turn about a vertical axis through point \( P \). The two disks rest on a rough horizontal surface; the coefficient of friction between the disks and the surface is \( \mu \). At time \( t = 0 \), the rod has an initial counterclockwise angular velocity \( \omega_0 \) about \( P \). The system is gradually brought to rest by friction. Develop expressions for the following quantities in terms of \( \mu \), \( m \), \( l \), \( g \), and \( \omega_0 \).

![Diagram](https://nerd-notes.com/wp-content/uploads/2025/03/twomassesonrodangularmomentumsystem.png)

**Part a)** The initial angular momentum of the system about the axis through \( P \) *(3 points)*

**Part b)** The frictional torque acting on the system about the axis through \( P \) *(3 points)*

**Part c)** The time \( T \) at which the system will come to rest. *(3 points)*


*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/79938/*