---
title: "A uniform horizontal shelf of mass M is attached to a vertical wall by a hinge at its left end and is supported by a vertical wire at its right end. A student intends to use the rotational equilibrium condition \\(\\sum \\tau = 0\\) to determine the magnitude of the tension in the wire. The student knows the mass of the shelf but does not know the magnitude or direction of the force exerted by the hinge on the shelf. Which of the following describes the most useful location for the axis of rotation and provides a correct justification?"
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url: "https://nerd-notes.com/ubq/113142/"
date_modified: "2026-05-05T04:26:56+00:00"
---

# A uniform horizontal shelf of mass M is attached to a vertical wall by a hinge at its left end and is supported by a vertical wire at its right end. A student intends to use the rotational equilibrium condition \(\sum \tau = 0\) to determine the magnitude of the tension in the wire. The student knows the mass of the shelf but does not know the magnitude or direction of the force exerted by the hinge on the shelf. Which of the following describes the most useful location for the axis of rotation and provides a correct justification?

A uniform horizontal shelf of mass M is attached to a vertical wall by a hinge at its left end and is supported by a vertical wire at its right end. A student intends to use the rotational equilibrium condition \(\sum \tau = 0\) to determine the magnitude of the tension in the wire. The student knows the mass of the shelf but does not know the magnitude or direction of the force exerted by the hinge on the shelf. Which of the following describes the most useful location for the axis of rotation and provides a correct justification?

![A horizontal rectangular shelf is attached to a vertical wall on the left by a small circular hinge. A thin vertical wire extends from the right end of the shelf to a point on the ceiling directly above it. A downward arrow labeled 'Mg' originates from the center of the shelf.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1777955215-5SFIdq.jpg)

- **A.** The hinge point, because the lever arm for the hinge force is zero, which eliminates the unknown hinge force from the torque equation.
- **B.** The center of the shelf, because the lever arm for the weight of the shelf is zero, which simplifies the equation by removing the gravitational torque.
- **C.** The attachment point of the wire, because it is the location of the force the student is trying to calculate.
- **D.** The hinge point, because in static equilibrium, the axis of rotation must be placed at a physical pivot or hinge.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/113142/*