---
title: "A student of mass \\(m\\) stands at the center of a circular platform of rotational inertia \\(I_0\\) that rotates freely about a vertical, frictionless axis through its center. At time \\(t = 0\\), when the platform rotates with angular speed \\(\\omega_0\\), the student begins walking radially outward at a constant speed relative to the platform. The graph shows the angular velocity \\(\\omega\\) of the platform as a function of time \\(t\\) as the student moves toward the platform’s edge.  Which of the following statements correctly describes a physical quantity of the platform-student system based on the graph?"
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url: "https://nerd-notes.com/ubq/124275/"
date_modified: "2026-09-28T14:04:37+00:00"
---

# A student of mass \(m\) stands at the center of a circular platform of rotational inertia \(I_0\) that rotates freely about a vertical, frictionless axis through its center. At time \(t = 0\), when the platform rotates with angular speed \(\omega_0\), the student begins walking radially outward at a constant speed relative to the platform. The graph shows the angular velocity \(\omega\) of the platform as a function of time \(t\) as the student moves toward the platform’s edge.

Which of the following statements correctly describes a physical quantity of the platform-student system based on the graph?

A student of mass \(m\) stands at the center of a circular platform of rotational inertia \(I_0\) that rotates freely about a vertical, frictionless axis through its center. At time \(t = 0\), when the platform rotates with angular speed \(\omega_0\), the student begins walking radially outward at a constant speed relative to the platform. The graph shows the angular velocity \(\omega\) of the platform as a function of time \(t\) as the student moves toward the platform's edge.

Which of the following statements correctly describes a physical quantity of the platform-student system based on the graph?

![A single two-dimensional Cartesian graph with two bare perpendicular coordinate axes without gridlines. The horizontal axis is labeled with the variable t at its right end, and the vertical axis is labeled with the Greek letter \omega at its top end. The intersection of the axes is labeled with the number 0. On the vertical axis, a tick mark is labeled \omega_0. A single smooth, solid curve begins on the vertical axis at the point (0, \omega_0) with a horizontal slope. As t increases, the curve extends continuously to the right, sloping downward with an initially downward curvature, then gradually leveling off toward the horizontal axis, remaining strictly above the horizontal axis throughout. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604277-1SYwAo.jpg)

- **A.** The magnitude of the angular acceleration of the platform is initially zero and increases during the early part of the motion because the magnitude of the slope of the curve increases from zero.
- **B.** The magnitude of the net external torque on the platform-student system is initially zero and increases during the early part of the motion because the magnitude of the slope of the curve increases from zero.
- **C.** The total rotational kinetic energy of the platform-student system remains constant because the area under the curve represents the net mechanical work done on the system.
- **D.** The angular displacement of the platform between \(t = 0\) and a later time \(t_1\) is equal to the slope of the secant line connecting those two points on the curve.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124275/*