---
title: "A motor delivers a constant mechanical power \\(P_0\\) to a spool of fixed rotational inertia \\(I\\) that rotates about a frictionless horizontal axle. As the spool winds thread of negligible mass from rest, an electronic sensor records that the spool’s angular acceleration decreases as its angular speed increases. Which of the following provides the correct physical explanation for why the angular acceleration decreases?"
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url: "https://nerd-notes.com/ubq/124317/"
date_modified: "2026-09-28T14:04:46+00:00"
---

# A motor delivers a constant mechanical power \(P_0\) to a spool of fixed rotational inertia \(I\) that rotates about a frictionless horizontal axle. As the spool winds thread of negligible mass from rest, an electronic sensor records that the spool’s angular acceleration decreases as its angular speed increases. Which of the following provides the correct physical explanation for why the angular acceleration decreases?

A motor delivers a constant mechanical power \(P_0\) to a spool of fixed rotational inertia \(I\) that rotates about a frictionless horizontal axle. As the spool winds thread of negligible mass from rest, an electronic sensor records that the spool's angular acceleration decreases as its angular speed increases. Which of the following provides the correct physical explanation for why the angular acceleration decreases?

![A side-view diagram of a cylindrical spool mounted horizontally on a central axle supported by two vertical ground stands. On the left end of the horizontal axle, a rectangular enclosure is labeled Motor. The spool consists of two thin circular outer flanges and a central cylindrical drum. A thin single line representing thread extends horizontally to the right from the bottom edge of the central drum. A curved rotation arrow is positioned above the top surface of the spool, curling over the top from right to left, labeled \(\omega\). A curved arrow next to \(\omega\) curls in the same direction, labeled \(\alpha\). The axle is depicted with dashed centerline segments indicating the axis of rotation. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604286-nWs55F.jpg)

- **A.** The motor delivers a constant torque because it operates at a constant power output, so the observed reduction in angular acceleration is caused by the thread increasing the rotational inertia of the spool.
- **B.** Mechanical power delivered to the spool is the product of torque and angular speed, which means a constant power output requires the applied torque to decrease as angular speed increases, thereby reducing the angular acceleration.
- **C.** A constant power delivery produces a constant rate of change of angular momentum, meaning that the applied torque remains constant while the angular acceleration diminishes to satisfy conservation of energy.
- **D.** As the spool spins faster, the increasing centripetal acceleration of the spool's mass requires a growing fraction of the motor's mechanical power, leaving less power available to produce tangential acceleration.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124317/*