---
title: "A fan with blades of length \\(L\\) rotates at a constant rate about its center. A small speck of dust is located on one of the blades at a distance of \\(\\dfrac{2}{3}L\\) from the axis of rotation. The fan is observed to complete \\(N\\) full revolutions in a time interval \\(\\Delta t\\). Which of the following is a correct expression for the speed \\(v\\) of the speck of dust?"
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url: "https://nerd-notes.com/ubq/111285/"
date_modified: "2026-04-10T01:20:26+00:00"
---

# A fan with blades of length \(L\) rotates at a constant rate about its center. A small speck of dust is located on one of the blades at a distance of \(\dfrac{2}{3}L\) from the axis of rotation. The fan is observed to complete \(N\) full revolutions in a time interval \(\Delta t\). Which of the following is a correct expression for the speed \(v\) of the speck of dust?

A fan with blades of length \(L\) rotates at a constant rate about its center. A small speck of dust is located on one of the blades at a distance of \(\dfrac{2}{3}L\) from the axis of rotation. The fan is observed to complete \(N\) full revolutions in a time interval \(\Delta t\). Which of the following is a correct expression for the speed \(v\) of the speck of dust?

![A diagram shows a single rectangular fan blade of length \(L\) extending horizontally to the right from a central axis of rotation. A point labeled \(P\) is marked on the blade at a distance exactly two-thirds of the way from the center to the tip. A dashed circle centered on the axis passes through point \(P\), representing its circular path. A curved arrow above the blade indicates a counter-clockwise direction of rotation. The distance from the center to the point \(P\) is labeled as \(r = \frac{2}{3}L\).](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1775784026-YkEiF8.jpg)

- **A.** \(v = \dfrac{2NL}{3\Delta t}\)
- **B.** \(v = \dfrac{4\pi NL}{3\Delta t}\)
- **C.** \(v = \dfrac{2\pi NL}{\Delta t}\)
- **D.** \(v = \dfrac{4\pi L}{3 N \Delta t}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/111285/*