---
title: "A stationary uniform solid sphere of mass \\(M\\) and radius \\(R\\) (with rotational inertia \\(I_{\\text{solid}} = \\dfrac{2}{5}MR^2\\)) rests on a rough horizontal surface. A cue delivers a sharp horizontal impulse \\(J\\) at the precise height \\(h\\) above the central horizontal axis where a thin spherical shell of the same mass and radius (with rotational inertia \\(I_{\\text{shell}} = \\dfrac{2}{3}MR^2\\)) would immediately roll without slipping with zero friction force during the strike. Because the sphere struck is solid, it initially slips before transitioning to pure rolling without slipping. What is the final speed \\(v_f\\) of the center of mass of the solid sphere once it rolls without slipping?"
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/124752/"
date_modified: "2026-09-28T14:09:59+00:00"
---

# A stationary uniform solid sphere of mass \(M\) and radius \(R\) (with rotational inertia \(I_{\text{solid}} = \dfrac{2}{5}MR^2\)) rests on a rough horizontal surface. A cue delivers a sharp horizontal impulse \(J\) at the precise height \(h\) above the central horizontal axis where a thin spherical shell of the same mass and radius (with rotational inertia \(I_{\text{shell}} = \dfrac{2}{3}MR^2\)) would immediately roll without slipping with zero friction force during the strike. Because the sphere struck is solid, it initially slips before transitioning to pure rolling without slipping. What is the final speed \(v_f\) of the center of mass of the solid sphere once it rolls without slipping?

A stationary uniform solid sphere of mass \(M\) and radius \(R\) (with rotational inertia \(I_{\text{solid}} = \dfrac{2}{5}MR^2\)) rests on a rough horizontal surface. A cue delivers a sharp horizontal impulse \(J\) at the precise height \(h\) above the central horizontal axis where a thin spherical shell of the same mass and radius (with rotational inertia \(I_{\text{shell}} = \dfrac{2}{3}MR^2\)) would immediately roll without slipping with zero friction force during the strike. Because the sphere struck is solid, it initially slips before transitioning to pure rolling without slipping. What is the final speed \(v_f\) of the center of mass of the solid sphere once it rolls without slipping?

- **A.** \(\dfrac{5}{7} \dfrac{J}{M}\)
- **B.** \(\dfrac{J}{M}\)
- **C.** \(\dfrac{25}{21} \dfrac{J}{M}\)
- **D.** \(\dfrac{5}{3} \dfrac{J}{M}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124752/*