---
title: "Three identical particles, each of mass \\(m\\), move at the same constant speed \\(v_0\\) in the \\(xy\\)-plane along three different straight paths:  Particle 1 moves in the \\(+x\\)-direction along the line \\(y = 2d\\). Particle 2 moves along the line \\(x + y = 2d\\) in the direction of increasing \\(x\\) and decreasing \\(y\\). Particle 3 moves in the \\(+y\\)-direction along the line \\(x = d\\).  Which of the following correctly ranks the magnitudes of the angular momenta \\(L_1\\), \\(L_2\\), and \\(L_3\\) of the particles about the origin?"
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url: "https://nerd-notes.com/ubq/120916/"
date_modified: "2026-08-23T04:44:18+00:00"
---

# Three identical particles, each of mass \(m\), move at the same constant speed \(v_0\) in the \(xy\)-plane along three different straight paths:

Particle 1 moves in the \(+x\)-direction along the line \(y = 2d\).
Particle 2 moves along the line \(x + y = 2d\) in the direction of increasing \(x\) and decreasing \(y\).
Particle 3 moves in the \(+y\)-direction along the line \(x = d\).

Which of the following correctly ranks the magnitudes of the angular momenta \(L_1\), \(L_2\), and \(L_3\) of the particles about the origin?

Three identical particles, each of mass \(m\), move at the same constant speed \(v_0\) in the \(xy\)-plane along three different straight paths:

Particle 1 moves in the \(+x\)-direction along the line \(y = 2d\).
Particle 2 moves along the line \(x + y = 2d\) in the direction of increasing \(x\) and decreasing \(y\).
Particle 3 moves in the \(+y\)-direction along the line \(x = d\).

Which of the following correctly ranks the magnitudes of the angular momenta \(L_1\), \(L_2\), and \(L_3\) of the particles about the origin?

![A Cartesian coordinate system with a horizontal x-axis and vertical y-axis intersecting at the origin labeled O. Tick marks on both axes are labeled d and 2d. A horizontal dashed line at y = 2d shows the path of Particle 1, with a circular dot at (0, 2d) and an arrow pointing to the right labeled with vector v_1. A downward-sloping dashed line connecting (0, 2d) and (2d, 0) shows the path of Particle 2, with a circular dot at (d, d) and an arrow pointing down and to the right along the line labeled with vector v_2. A vertical dashed line at x = d shows the path of Particle 3, with a circular dot at (d, 0) and an arrow pointing upward labeled with vector v_3. All velocity arrows have identical lengths. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787460257-zq2D47.jpg)

- **A.** \(L_2 > L_1 > L_3\)
- **B.** \(L_1 = L_2 > L_3\)
- **C.** \(L_1 > L_3 > L_2\)
- **D.** \(L_1 > L_2 > L_3\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120916/*