---
title: "A flywheel of unknown rotational inertia \\(I\\) is mounted on a frictionless horizontal axle and is initially at rest. A known constant net torque \\(\\tau\\) is applied to the flywheel, causing it to rotate. In a series of trials, a student measures the angular displacement \\(\\Delta\\theta\\) through which the flywheel rotates and its corresponding final angular speed \\(\\omega\\). Which of the following pairs of quantities, when plotted on the vertical and horizontal axes, will produce a linear graph, and what is the correct expression for \\(I\\) in terms of the slope \\(S\\) of the best-fit line?"
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url: "https://nerd-notes.com/ubq/121034/"
date_modified: "2026-08-23T04:49:11+00:00"
---

# A flywheel of unknown rotational inertia \(I\) is mounted on a frictionless horizontal axle and is initially at rest. A known constant net torque \(\tau\) is applied to the flywheel, causing it to rotate. In a series of trials, a student measures the angular displacement \(\Delta\theta\) through which the flywheel rotates and its corresponding final angular speed \(\omega\). Which of the following pairs of quantities, when plotted on the vertical and horizontal axes, will produce a linear graph, and what is the correct expression for \(I\) in terms of the slope \(S\) of the best-fit line?

A flywheel of unknown rotational inertia \(I\) is mounted on a frictionless horizontal axle and is initially at rest. A known constant net torque \(\tau\) is applied to the flywheel, causing it to rotate. In a series of trials, a student measures the angular displacement \(\Delta\theta\) through which the flywheel rotates and its corresponding final angular speed \(\omega\). Which of the following pairs of quantities, when plotted on the vertical and horizontal axes, will produce a linear graph, and what is the correct expression for \(I\) in terms of the slope \(S\) of the best-fit line?

- **A.** Vertical axis: \(\omega\); Horizontal axis: \(\Delta\theta\); \(I = \dfrac{2\tau}{S^2}\)
- **B.** Vertical axis: \(\omega^2\); Horizontal axis: \(\Delta\theta\); \(I = \dfrac{2\tau}{S}\)
- **C.** Vertical axis: \(\omega^2\); Horizontal axis: \(\Delta\theta\); \(I = \dfrac{\tau}{2S}\)
- **D.** Vertical axis: \(\Delta\theta\); Horizontal axis: \(\omega^2\); \(I = \dfrac{2\tau}{S}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/121034/*