---
title: "A ball of radius \\( r \\) rolls on the inside of a track of radius \\( R \\). If the ball starts from rest at the vertical edge of the track, what will be its speed when it reaches the lowest point of the track, rolling without slipping?"
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url: "https://nerd-notes.com/ubq/84493/"
date_modified: "2026-01-15T02:51:51+00:00"
---

# A ball of radius \( r \) rolls on the inside of a track of radius \( R \). If the ball starts from rest at the vertical edge of the track, what will be its speed when it reaches the lowest point of the track, rolling without slipping?

A ball of radius \( r \) rolls on the inside of a circular track of radius \( R \). If the ball starts from rest at the left vertical edge of the track, what will be its speed when it reaches the lowest point of the track, rolling without slipping? For a solid spherical ball, the moment of inertia is \(\frac{2}{5} m r^2\).

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

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