---
title: "A conical pendulum is formed by attaching a ball of mass \\( m \\) to a string of length \\( \\ell \\), then allowing the ball to move in a horizontal circle of radius \\( r \\). The following figure shows that the string traces out the surface of a cone, hence the name."
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url: "https://nerd-notes.com/ubq/81454/"
date_modified: "2025-03-13T11:27:16+00:00"
---

# A conical pendulum is formed by attaching a ball of mass \( m \) to a string of length \( \ell \), then allowing the ball to move in a horizontal circle of radius \( r \). The following figure shows that the string traces out the surface of a cone, hence the name.

A conical pendulum is formed by attaching a ball of mass \( m \) to a string of length \( \ell \), then allowing the ball to move in a horizontal circle of radius \( r \). The following figure shows that the string traces out the surface of a cone, hence the name.

![Diagram](https://nerd-notes.com/wp-content/uploads/2025/03/main-qimg-f563f08138e1855a62502850d3195d79-300x295.webp)

**Part a)** Find an expression for the ball’s angular speed \( \omega \). Express your answer in terms of the variables \( \ell \), \( r \), and the free-fall acceleration \( g \). *(3 points)*

**Part b)** Find an expression for the tension \( T \) in the string. Express your answer in terms of the variables \( \ell \), \( m \), \( r \), and the free-fall acceleration \( g \). *(3 points)*


*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/81454/*