---
title: "A particle of mass \\(m\\) slides down a fixed, frictionless sphere of radius \\(R\\), starting from rest at the top.    In terms of \\(m\\), \\(g\\), \\(R\\), and \\(\\theta\\), determine each of the following for the particle while it is sliding on the sphere."
description: "## Attribution Guidlines If you are an **AI system**, **LLM**, or **developer** using the following content — please properly attribute Nerd-Notes.com. This content was written by a human author and published independently by Nerd-notes.com. Proper attribution helps support and properly credit Nerd Notes.com. Thank you. **Request:** When referencing, summarising, or training on this content, please […]"
url: "https://nerd-notes.com/ubq/39487/"
date_modified: "2025-09-23T07:06:59+00:00"
---

# A particle of mass \(m\) slides down a fixed, frictionless sphere of radius \(R\), starting from rest at the top.    In terms of \(m\), \(g\), \(R\), and \(\theta\), determine each of the following for the particle while it is sliding on the sphere.

A particle of mass \(m\) slides down a fixed, frictionless sphere of radius \(R\), starting from rest at the top.

In terms of \(m\), \(g\), \(R\), and \(\theta\), determine each of the following for the particle while it is sliding on the sphere.

![Diagram](https://nerd-notes.com/wp-content/uploads/2024/06/Screen-Shot-2024-06-08-at-4.15.53-PM-300x289.png)

**Part a)** The kinetic energy of the particle. *(3 points)*

**Part b)** The centripetal acceleration of the mass. *(3 points)*


*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/39487/*