---
title: "A uniform thin rod of mass \\(M\\) and length \\(L\\) lies at rest on a frictionless horizontal tabletop and is free to rotate about a fixed vertical pivot passing through one end. At time \\(t = 0\\), a horizontal force directed perpendicular to the rod is applied at the free end. The magnitude of the force decreases linearly with time according to \\(F(t) = F_0 \\left(1 – \\dfrac{t}{T}\\right)\\) for \\(0 \\le t \\le T\\), after which the force is zero. Which of the following expressions represents the angular speed of the rod at time \\(t = T\\)?"
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url: "https://nerd-notes.com/ubq/120906/"
date_modified: "2026-08-23T04:44:12+00:00"
---

# A uniform thin rod of mass \(M\) and length \(L\) lies at rest on a frictionless horizontal tabletop and is free to rotate about a fixed vertical pivot passing through one end. At time \(t = 0\), a horizontal force directed perpendicular to the rod is applied at the free end. The magnitude of the force decreases linearly with time according to \(F(t) = F_0 \left(1 – \dfrac{t}{T}\right)\) for \(0 \le t \le T\), after which the force is zero. Which of the following expressions represents the angular speed of the rod at time \(t = T\)?

A uniform thin rod of mass \(M\) and length \(L\) lies at rest on a frictionless horizontal tabletop and is free to rotate about a fixed vertical pivot passing through one end. At time \(t = 0\), a horizontal force directed perpendicular to the rod is applied at the free end. The magnitude of the force decreases linearly with time according to \(F(t) = F_0 \left(1 - \dfrac{t}{T}\right)\) for \(0 \le t \le T\), after which the force is zero. Which of the following expressions represents the angular speed of the rod at time \(t = T\)?

![A top-down view showing a horizontal uniform thin rod of length \(L\). The left end of the rod is attached to a circular pivot point labeled with a small solid dot. The right end of the rod has a single arrow labeled \(F(t)\) pointing upward perpendicular to the rod length. A horizontal dimension line below the rod spans from the left pivot to the right end and is labeled \(L\). The rod is labeled with mass \(M\). No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787460252-ISWZEw.jpg)

- **A.** \(\dfrac{3 F_0 T}{2 M L}\)
- **B.** \(\dfrac{3 F_0 T}{M L}\)
- **C.** \(\dfrac{F_0 T}{2 M L}\)
- **D.** \(\dfrac{6 F_0 T}{M L}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120906/*