---
title: "A uniform solid sphere of mass \\(M\\) and radius \\(R\\) is launched horizontally across a flat, rough floor at time \\(t = 0\\) with an initial translational speed \\(v_0\\) and zero initial angular velocity (\\(\\omega_0 = 0\\)). The coefficient of kinetic friction between the sphere and the floor is a constant \\(\\mu_k\\), and air resistance is negligible. At time \\(t_1\\), the sphere transitions to rolling without slipping. Which of the following graphs best represents the sphere’s translational speed \\(v(t)\\) and tangential speed of rotation \\(R\\omega(t)\\) as functions of time \\(t\\) for \\(t \\ge 0\\)?"
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url: "https://nerd-notes.com/ubq/120957/"
date_modified: "2026-08-23T04:44:41+00:00"
---

# A uniform solid sphere of mass \(M\) and radius \(R\) is launched horizontally across a flat, rough floor at time \(t = 0\) with an initial translational speed \(v_0\) and zero initial angular velocity (\(\omega_0 = 0\)). The coefficient of kinetic friction between the sphere and the floor is a constant \(\mu_k\), and air resistance is negligible. At time \(t_1\), the sphere transitions to rolling without slipping. Which of the following graphs best represents the sphere’s translational speed \(v(t)\) and tangential speed of rotation \(R\omega(t)\) as functions of time \(t\) for \(t \ge 0\)?

A uniform solid sphere of mass \(M\) and radius \(R\) is launched horizontally across a flat, rough floor at time \(t = 0\) with an initial translational speed \(v_0\) and zero initial angular velocity (\(\omega_0 = 0\)). The coefficient of kinetic friction between the sphere and the floor is a constant \(\mu_k\), and air resistance is negligible. At time \(t_1\), the sphere transitions to rolling without slipping. Which of the following graphs best represents the sphere's translational speed \(v(t)\) and tangential speed of rotation \(R\omega(t)\) as functions of time \(t\) for \(t \ge 0\)?

- **A.** Graph A
- **B.** Graph B
- **C.** Graph C
- **D.** Graph D

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120957/*