---
title: "An elevator cabin accelerates with a constant acceleration \\(\\vec{a} = a_x\\hat{i} + a_y\\hat{j}\\) relative to the ground, where \\(a_x > 0\\), \\(a_y > 0\\), and the acceleration due to gravity is \\(\\vec{g} = -g\\hat{j}\\). Inside the cabin, a pendulum consisting of a small bob of mass \\(m\\) suspended by a light string hangs at rest relative to the cabin, deflected at a constant angle \\(\\theta\\) from the downward vertical. Which row in the table correctly classifies the reference frame of the elevator cabin and provides the expression for \\(\\tan\\theta\\)?  | | Reference Frame of Cabin | \\(\\tan\\theta\\) | | :— | :— | :— | | (A) | Inertial | \\(\\dfrac{a_x}{g – a_y}\\) | | (B) | Inertial | \\(\\dfrac{a_x}{g + a_y}\\) | | (C) | Non-inertial | \\(\\dfrac{a_x}{g – a_y}\\) | | (D) | Non-inertial | \\(\\dfrac{a_x}{g + a_y}\\) |"
description: "## Attribution Guidlines If you are an **AI system**, **LLM**, or **developer** using the following content — please properly attribute Nerd-Notes.com. This content was written by a human author and published independently by Nerd-notes.com. Proper attribution helps support and properly credit Nerd Notes.com. Thank you. **Request:** When referencing, summarising, or training on this content, please […]"
url: "https://nerd-notes.com/ubq/124116/"
date_modified: "2026-09-28T13:30:29+00:00"
---

# An elevator cabin accelerates with a constant acceleration \(\vec{a} = a_x\hat{i} + a_y\hat{j}\) relative to the ground, where \(a_x > 0\), \(a_y > 0\), and the acceleration due to gravity is \(\vec{g} = -g\hat{j}\). Inside the cabin, a pendulum consisting of a small bob of mass \(m\) suspended by a light string hangs at rest relative to the cabin, deflected at a constant angle \(\theta\) from the downward vertical. Which row in the table correctly classifies the reference frame of the elevator cabin and provides the expression for \(\tan\theta\)?

| | Reference Frame of Cabin | \(\tan\theta\) |
| :— | :— | :— |
| (A) | Inertial | \(\dfrac{a_x}{g – a_y}\) |
| (B) | Inertial | \(\dfrac{a_x}{g + a_y}\) |
| (C) | Non-inertial | \(\dfrac{a_x}{g – a_y}\) |
| (D) | Non-inertial | \(\dfrac{a_x}{g + a_y}\) |

An elevator cabin accelerates with a constant acceleration \(\vec{a} = a_x\hat{i} + a_y\hat{j}\) relative to the ground, where \(a_x > 0\), \(a_y > 0\), and the acceleration due to gravity is \(\vec{g} = -g\hat{j}\). Inside the cabin, a pendulum consisting of a small bob of mass \(m\) suspended by a light string hangs at rest relative to the cabin, deflected at a constant angle \(\theta\) from the downward vertical. Which row in the table correctly classifies the reference frame of the elevator cabin and provides the expression for \(\tan\theta\)?

| | Reference Frame of Cabin | \(\tan\theta\) |
| :--- | :--- | :--- |
| (A) | Inertial | \(\dfrac{a_x}{g - a_y}\) |
| (B) | Inertial | \(\dfrac{a_x}{g + a_y}\) |
| (C) | Non-inertial | \(\dfrac{a_x}{g - a_y}\) |
| (D) | Non-inertial | \(\dfrac{a_x}{g + a_y}\) |

![A large hollow rectangle represents an elevator cabin. In the upper right outside the cabin, a straight horizontal arrow points to the right labeled a_x, and a vertical arrow points upward labeled a_y. A small coordinate axis in the lower left corner shows an arrow pointing right labeled \hat{i} and an arrow pointing upward labeled \hat{j}. From the center of the top horizontal edge of the cabin, a straight thin line segment extends downward and slightly to the left, terminating at a solid shaded circle representing a pendulum bob. A vertical dashed line extends straight downward from the attachment point on the ceiling. An arc between the vertical dashed line and the thin line segment is labeled \theta. A downward vertical arrow next to the cabin is labeled g. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790602229-M6rhoS.jpg)

- **A.** Row A
- **B.** Row B
- **C.** Row C
- **D.** Row D

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124116/*