---
title: "A flat circular turntable rotates about a fixed vertical axis passing perpendicularly through its center. Starting from rest at time \\(t = 0\\), the turntable experiences a time-dependent angular acceleration given by \\(\\alpha(t) = bt^2\\), where \\(b = 9.0\\text{ rad/s}^4\\). Three small markers, \\(A\\), \\(B\\), and \\(C\\), are placed on the turntable at the radial distances and observed at the times specified in the table below.  | Marker | Distance from Axis (\\(r\\)) | Time of Observation (\\(t\\)) | | :— | :— | :— | | \\(A\\) | \\(0.60\\text{ m}\\) | \\(1.0\\text{ s}\\) | | \\(B\\) | \\(0.20\\text{ m}\\) | \\(1.0\\text{ s}\\) | | \\(C\\) | \\(0.010\\text{ m}\\) | \\(2.0\\text{ s}\\) |  Which of the following correctly ranks the magnitudes of the total linear acceleration \\(a\\) of the three markers at their respective times of observation?"
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url: "https://nerd-notes.com/ubq/124428/"
date_modified: "2026-09-28T14:05:27+00:00"
---

# A flat circular turntable rotates about a fixed vertical axis passing perpendicularly through its center. Starting from rest at time \(t = 0\), the turntable experiences a time-dependent angular acceleration given by \(\alpha(t) = bt^2\), where \(b = 9.0\text{ rad/s}^4\). Three small markers, \(A\), \(B\), and \(C\), are placed on the turntable at the radial distances and observed at the times specified in the table below.

| Marker | Distance from Axis (\(r\)) | Time of Observation (\(t\)) |
| :— | :— | :— |
| \(A\) | \(0.60\text{ m}\) | \(1.0\text{ s}\) |
| \(B\) | \(0.20\text{ m}\) | \(1.0\text{ s}\) |
| \(C\) | \(0.010\text{ m}\) | \(2.0\text{ s}\) |

Which of the following correctly ranks the magnitudes of the total linear acceleration \(a\) of the three markers at their respective times of observation?

A flat circular turntable rotates about a fixed vertical axis passing perpendicularly through its center. Starting from rest at time \(t = 0\), the turntable experiences a time-dependent angular acceleration given by \(\alpha(t) = bt^2\), where \(b = 9.0\text{ rad/s}^4\). Three small markers, \(A\), \(B\), and \(C\), are placed on the turntable at the radial distances and observed at the times specified in the table below.

| Marker | Distance from Axis (\(r\)) | Time of Observation (\(t\)) |
| :--- | :--- | :--- |
| \(A\) | \(0.60\text{ m}\) | \(1.0\text{ s}\) |
| \(B\) | \(0.20\text{ m}\) | \(1.0\text{ s}\) |
| \(C\) | \(0.010\text{ m}\) | \(2.0\text{ s}\) |

Which of the following correctly ranks the magnitudes of the total linear acceleration \(a\) of the three markers at their respective times of observation?

- **A.** \(a_A > a_B > a_C\)
- **B.** \(a_C > a_A > a_B\)
- **C.** \(a_C > a_B > a_A\)
- **D.** \(a_A > a_C > a_B\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124428/*