---
title: "A horizontal turntable of rotational inertia \\(I\\) rotates freely about a vertical, frictionless axle with initial angular speed \\(\\omega_0\\). A second, initially stationary disk of identical rotational inertia \\(I\\) is dropped gently and coaxially onto the turntable. Due to friction between their surfaces, the two disks slip against each other for a brief time before rotating together with a common final angular speed. Which of the following statements correctly relates the final rotational kinetic energy \\(K_f\\) of the two-disk system to its initial rotational kinetic energy \\(K_i\\) and provides the correct physical justification?"
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url: "https://nerd-notes.com/ubq/120908/"
date_modified: "2026-08-23T04:44:13+00:00"
---

# A horizontal turntable of rotational inertia \(I\) rotates freely about a vertical, frictionless axle with initial angular speed \(\omega_0\). A second, initially stationary disk of identical rotational inertia \(I\) is dropped gently and coaxially onto the turntable. Due to friction between their surfaces, the two disks slip against each other for a brief time before rotating together with a common final angular speed. Which of the following statements correctly relates the final rotational kinetic energy \(K_f\) of the two-disk system to its initial rotational kinetic energy \(K_i\) and provides the correct physical justification?

A horizontal turntable of rotational inertia \(I\) rotates freely about a vertical, frictionless axle with initial angular speed \(\omega_0\). A second, initially stationary disk of identical rotational inertia \(I\) is dropped gently and coaxially onto the turntable. Due to friction between their surfaces, the two disks slip against each other for a brief time before rotating together with a common final angular speed. Which of the following statements correctly relates the final rotational kinetic energy \(K_f\) of the two-disk system to its initial rotational kinetic energy \(K_i\) and provides the correct physical justification?

![A three-dimensional schematic showing two identical circular flat disks aligned along a single vertical central dashed axis. The lower disk is mounted horizontally on a thin vertical cylindrical axle that extends downward into a small square support base. A curved arrow above the lower disk indicates counterclockwise rotation about the vertical axis with label \(\omega_0\). The upper disk is positioned directly above the lower disk, oriented horizontally, centered on the same vertical dashed axis. A straight downward vertical arrow labeled \(\vec{v}\) is positioned between the upper and lower disks, directed toward the top surface of the lower disk. Both disks have label \(I\) indicated to their right. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787460252-4N8t1z.jpg)

- **A.** \(K_f = K_i\) because the net external torque on the two-disk system is zero, so mechanical energy must be conserved whenever angular momentum is conserved.
- **B.** \(K_f = \dfrac{1}{2}K_i\) because the frictional torque between the slipping surfaces does net negative work on the system, dissipating mechanical energy as thermal energy.
- **C.** \(K_f = \dfrac{1}{2}K_i\) because the downward gravitational force does negative work on the dropped disk to bring both disks into vertical equilibrium.
- **D.** \(K_f = 2K_i\) because the total rotational inertia of the system doubles while the net angular momentum remains constant.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120908/*