---
title: "A small block of mass \\(m\\) on a frictionless horizontal table rotates in a circle of radius \\(R_0\\) attached to a string that passes through a central hole in the table. The string is slowly pulled downward through the hole, decreasing the radius of the circular path. Student 1 argues that the tangential speed \\(v\\) must remain constant because the tension force is perpendicular to the velocity and therefore does no work. Student 2 argues that the angular speed \\(\\omega\\) must remain constant because the tension force is directed toward the central hole and therefore exerts zero torque. Which of the following statements correctly explains why both students’ arguments are incorrect?"
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url: "https://nerd-notes.com/ubq/120808/"
date_modified: "2026-08-23T04:43:25+00:00"
---

# A small block of mass \(m\) on a frictionless horizontal table rotates in a circle of radius \(R_0\) attached to a string that passes through a central hole in the table. The string is slowly pulled downward through the hole, decreasing the radius of the circular path. Student 1 argues that the tangential speed \(v\) must remain constant because the tension force is perpendicular to the velocity and therefore does no work. Student 2 argues that the angular speed \(\omega\) must remain constant because the tension force is directed toward the central hole and therefore exerts zero torque. Which of the following statements correctly explains why both students’ arguments are incorrect?

A small block of mass \(m\) on a frictionless horizontal table rotates in a circle of radius \(R_0\) attached to a string that passes through a central hole in the table. The string is slowly pulled downward through the hole, decreasing the radius of the circular path. Student 1 argues that the tangential speed \(v\) must remain constant because the tension force is perpendicular to the velocity and therefore does no work. Student 2 argues that the angular speed \(\omega\) must remain constant because the tension force is directed toward the central hole and therefore exerts zero torque. Which of the following statements correctly explains why both students' arguments are incorrect?

![A horizontal circular tabletop viewed from an oblique overhead perspective. At the center of the tabletop is a small circular hole. A small solid rectangular block is positioned on the table surface at a radial distance from the hole. A single taut straight line representing a string connects the center of the block to the central hole. A dashed circle centered on the hole passes through the block to represent the circular path. Beneath the table, a vertical straight line representing the string extends straight downward from the central hole, terminating in a downward-pointing arrow. A straight dimension arrow extends from the central hole to the block, labeled R_0. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787460205-RliCfS.jpg)

- **A.** The tension force exerts a nonzero torque about the central hole because the string's line of action shifts inward during the pull, while the tangential speed decreases to conserve total mechanical energy.
- **B.** The tension force does zero net work because the displacement over each complete revolution is zero, but the angular speed decreases because the centripetal acceleration must remain constant.
- **C.** The tension force does positive work because the block has an inward radial displacement along the line of the force, increasing its speed, while zero net torque conserves angular momentum \(mr^2\omega\), forcing the angular speed to increase as the radius decreases.
- **D.** The tension force does no work along the circular path, but linear momentum is conserved in the tangential direction, causing the tangential speed to increase while the angular speed decreases proportionally.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120808/*