---
title: "A hoop with a mass m and unknown radius is rolling without slipping on a flat surface with an angular speed w. The hoop encounters a hill and continues to roll without slipping until it reaches a maximum height h. "
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url: "https://nerd-notes.com/ubq/29637/"
date_modified: "2024-05-29T09:58:03+00:00"
---

# A hoop with a mass m and unknown radius is rolling without slipping on a flat surface with an angular speed w. The hoop encounters a hill and continues to roll without slipping until it reaches a maximum height h. 

A hoop with a mass \(m\) and unknown radius is rolling without slipping on a flat surface with an angular speed \(\omega\)*.* The hoop encounters a hill and continues to roll without slipping until it reaches a maximum height \(h\)*.*

![Diagram](https://nerd-notes.com/wp-content/uploads/2024/03/Screenshot-2024-03-28-at-8.53.18-PM-e1711944331966-300x90.png)

**Part a)** Derive an expression for the radius of the hoop in terms of given quantities and fundamental constants. *(3 points)*

**Part b)** What direction does friction point while the ball is rolling up the ramp? Explain your reasoning. *(3 points)*

**Part c)** After reaching the maximum height, the ball begins to roll back down. What direction does friction point while the ball is rolling down the ramp? Explain your reasoning. *(3 points)*


*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/29637/*