---
title: "A small bead of mass \\(m\\) slides along the frictionless outer surface of a stationary vertical circular hoop of radius \\(R = 5.0\\text{ m}\\). The bead is initially at the highest point of the hoop and is given an initial horizontal speed \\(v_0 = 3.5\\text{ m/s}\\). Let \\(\\theta\\) be the angle between the upward vertical and the position vector of the bead measured from the center of the hoop. At what angle \\(\\theta\\) does the bead lose contact with the hoop?"
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url: "https://nerd-notes.com/ubq/124173/"
date_modified: "2026-09-28T13:30:53+00:00"
---

# A small bead of mass \(m\) slides along the frictionless outer surface of a stationary vertical circular hoop of radius \(R = 5.0\text{ m}\). The bead is initially at the highest point of the hoop and is given an initial horizontal speed \(v_0 = 3.5\text{ m/s}\). Let \(\theta\) be the angle between the upward vertical and the position vector of the bead measured from the center of the hoop. At what angle \(\theta\) does the bead lose contact with the hoop?

A small bead of mass \(m\) slides along the frictionless outer surface of a stationary vertical circular hoop of radius \(R = 5.0\text{ m}\). The bead is initially at the highest point of the hoop and is given an initial horizontal speed \(v_0 = 3.5\text{ m/s}\). Let \(\theta\) be the angle between the upward vertical and the position vector of the bead measured from the center of the hoop. At what angle \(\theta\) does the bead lose contact with the hoop?

![A vertical circle with a small filled circular bead resting on its top rim. A horizontal arrow pointing to the right from the bead is labeled \(v_0\). A dashed vertical centerline passes from the center dot of the circle to the top rim. An arrow pointing from the center of the circle to the perimeter is labeled \(R\). Along the upper-right curved perimeter, a second small bead is shown at a position displaced clockwise from the top rim. A solid straight line segment connects the center of the circle to this second bead. An arc between the vertical dashed centerline and this solid line segment is labeled \(\theta\). No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790602252-tV7EcY.jpg)

- **A.** \(23.6^\circ\)
- **B.** \(37.7^\circ\)
- **C.** \(41.4^\circ\)
- **D.** \(48.2^\circ\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124173/*