---
title: "A particle of mass \\(m\\) moves in the \\(xy\\)-plane along the horizontal line \\(y = d\\) in the positive \\(x\\)-direction with a speed given as a function of time \\(t\\) by \\(v(t) = C t^2\\), where \\(C\\) is a positive constant. Which of the following expressions represents the magnitude of the rate of change of the particle’s angular momentum about the origin, \\(\\dfrac{dL}{dt}\\), as a function of time?"
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url: "https://nerd-notes.com/ubq/117630/"
date_modified: "2026-08-04T07:49:22+00:00"
---

# A particle of mass \(m\) moves in the \(xy\)-plane along the horizontal line \(y = d\) in the positive \(x\)-direction with a speed given as a function of time \(t\) by \(v(t) = C t^2\), where \(C\) is a positive constant. Which of the following expressions represents the magnitude of the rate of change of the particle’s angular momentum about the origin, \(\dfrac{dL}{dt}\), as a function of time?

A particle of mass \(m\) moves in the \(xy\)-plane along the horizontal line \(y = d\) in the positive \(x\)-direction with a speed given as a function of time \(t\) by \(v(t) = C t^2\), where \(C\) is a positive constant. Which of the following expressions represents the magnitude of the rate of change of the particle's angular momentum about the origin, \(\dfrac{dL}{dt}\), as a function of time?

![A two-dimensional Cartesian coordinate system with horizontal axis x and vertical axis y intersecting at an origin labeled O. A horizontal line parallel to the x-axis is located at vertical coordinate y = d. A solid circular dot representing a particle of mass m is positioned on the horizontal line at an arbitrary positive x-coordinate. A horizontal velocity vector arrow labeled v(t) points to the right from the particle along the line y = d. A vertical dashed line segment extends along the y-axis from the origin O up to the line y = d, labeled with distance d. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785829762-D9rzoS.jpg)

- **A.** \(\dfrac{1}{3} m C d t^3\)
- **B.** \(m C d t^2\)
- **C.** \(m C d t\)
- **D.** \(2 m C d t\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117630/*