---
title: "A student performs an experiment to determine the rotational inertia \\(I\\) of a rigid flywheel that rotates about a fixed, frictionless axle. The flywheel is initially rotating with an unknown, non-zero initial angular speed \\(\\omega_0\\). Starting at time \\(t = 0\\), a known constant net torque \\(\\tau_0\\) is applied to the flywheel in the direction of rotation, and an optical sensor measures the angular displacement \\(\\Delta\\theta\\) from its orientation at \\(t = 0\\) as a function of time \\(t\\). Which of the following pairs of quantities, when plotted, will produce a linear graph, and what is the correct expression for determining the rotational inertia \\(I\\) from the slope \\(m\\) of the best-fit line?"
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url: "https://nerd-notes.com/ubq/120851/"
date_modified: "2026-08-23T04:43:37+00:00"
---

# A student performs an experiment to determine the rotational inertia \(I\) of a rigid flywheel that rotates about a fixed, frictionless axle. The flywheel is initially rotating with an unknown, non-zero initial angular speed \(\omega_0\). Starting at time \(t = 0\), a known constant net torque \(\tau_0\) is applied to the flywheel in the direction of rotation, and an optical sensor measures the angular displacement \(\Delta\theta\) from its orientation at \(t = 0\) as a function of time \(t\). Which of the following pairs of quantities, when plotted, will produce a linear graph, and what is the correct expression for determining the rotational inertia \(I\) from the slope \(m\) of the best-fit line?

A student performs an experiment to determine the rotational inertia \(I\) of a rigid flywheel that rotates about a fixed, frictionless axle. The flywheel is initially rotating with an unknown, non-zero initial angular speed \(\omega_0\). Starting at time \(t = 0\), a known constant net torque \(\tau_0\) is applied to the flywheel in the direction of rotation, and an optical sensor measures the angular displacement \(\Delta\theta\) from its orientation at \(t = 0\) as a function of time \(t\). Which of the following pairs of quantities, when plotted, will produce a linear graph, and what is the correct expression for determining the rotational inertia \(I\) from the slope \(m\) of the best-fit line?

![A circular flywheel is mounted vertically on a horizontal central axle supported by a rigid vertical post. A wrapped cord extends tangentially from the flywheel rim downward, with an arrow labeled \tau_0 indicating applied torque. A small rectangular optical sensor is positioned near the outer edge of the wheel facing the rim. A curved arrow near the top of the wheel indicates rotational direction. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787460217-Ka4mwp.jpg)

- **A.** Plot \(\Delta\theta\) on the vertical axis versus \(t^2\) on the horizontal axis; \(I = \dfrac{\tau_0}{2m}\)
- **B.** Plot \(\dfrac{\Delta\theta}{t}\) on the vertical axis versus \(t\) on the horizontal axis; \(I = \dfrac{\tau_0}{2m}\)
- **C.** Plot \(\dfrac{\Delta\theta}{t}\) on the vertical axis versus \(t\) on the horizontal axis; \(I = \dfrac{\tau_0}{m}\)
- **D.** Plot \(\dfrac{\Delta\theta}{t}\) on the vertical axis versus \(\dfrac{1}{t}\) on the horizontal axis; \(I = \dfrac{2\tau_0}{m}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120851/*