---
title: "A rigid disk of radius \\(R\\) rotates in a vertical plane about a fixed horizontal axle through its center. At the instant shown, a point \\(P\\) on the outer rim of the disk is at the highest position directly above the axle, moving to the right with instantaneous speed \\(v\\) and angular speed \\(\\omega\\). The disk is slowing down with a constant angular deceleration of magnitude \\(\\alpha\\). Which of the following correctly identifies the direction of the total linear acceleration vector \\(\\vec{a}\\) of point \\(P\\) at this instant and gives the correct expression for \\(\\tan\\phi\\), where \\(\\phi\\) is the angle of \\(\\vec{a}\\) measured from the inward radial line toward the axle?"
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url: "https://nerd-notes.com/ubq/120845/"
date_modified: "2026-08-23T04:43:36+00:00"
---

# A rigid disk of radius \(R\) rotates in a vertical plane about a fixed horizontal axle through its center. At the instant shown, a point \(P\) on the outer rim of the disk is at the highest position directly above the axle, moving to the right with instantaneous speed \(v\) and angular speed \(\omega\). The disk is slowing down with a constant angular deceleration of magnitude \(\alpha\). Which of the following correctly identifies the direction of the total linear acceleration vector \(\vec{a}\) of point \(P\) at this instant and gives the correct expression for \(\tan\phi\), where \(\phi\) is the angle of \(\vec{a}\) measured from the inward radial line toward the axle?

A rigid disk of radius \(R\) rotates in a vertical plane about a fixed horizontal axle through its center. At the instant shown, a point \(P\) on the outer rim of the disk is at the highest position directly above the axle, moving to the right with instantaneous speed \(v\) and angular speed \(\omega\). The disk is slowing down with a constant angular deceleration of magnitude \(\alpha\). Which of the following correctly identifies the direction of the total linear acceleration vector \(\vec{a}\) of point \(P\) at this instant and gives the correct expression for \(\tan\phi\), where \(\phi\) is the angle of \(\vec{a}\) measured from the inward radial line toward the axle?

![A circular disk of radius \(R\) is shown in a vertical plane with its center labeled \(O\). A horizontal dashed line and a vertical dashed line intersect at the center \(O\). At the very top perimeter of the disk is a solid point labeled \(P\). A straight solid arrow originates at point \(P\), points horizontally to the right, and is labeled \(\vec{v}\). A curved arrow near the top edge indicates clockwise rotation. A straight dimension line with arrowheads extends from the center \(O\) to the perimeter labeled \(R\). No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787460215-A2POGK.jpg)

- **A.** Direction: Downward and to the left; Value: \(\tan\phi = \dfrac{\alpha}{\omega^2}\)
- **B.** Direction: Downward and to the left; Value: \(\tan\phi = \dfrac{\omega^2}{\alpha}\)
- **C.** Direction: Downward and to the right; Value: \(\tan\phi = \dfrac{\alpha}{\omega^2}\)
- **D.** Direction: Downward and to the right; Value: \(\tan\phi = \dfrac{\omega^2}{\alpha}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120845/*