---
title: "A person stands at rest on a low-friction turntable that is free to rotate about a vertical axis, holding a bicycle wheel that is spinning rapidly about a vertical axle with angular momentum of magnitude \\(L_0\\) directed upward. When the person inverts the wheel upside down by \\(180^\\circ\\) so that its angular momentum points downward with magnitude \\(L_0\\), the person and turntable begin rotating such that their angular momentum is directed upward with magnitude \\(2L_0\\). Which of the following statements provides the correct physical explanation for this observation?"
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url: "https://nerd-notes.com/ubq/124241/"
date_modified: "2026-09-28T14:04:27+00:00"
---

# A person stands at rest on a low-friction turntable that is free to rotate about a vertical axis, holding a bicycle wheel that is spinning rapidly about a vertical axle with angular momentum of magnitude \(L_0\) directed upward. When the person inverts the wheel upside down by \(180^\circ\) so that its angular momentum points downward with magnitude \(L_0\), the person and turntable begin rotating such that their angular momentum is directed upward with magnitude \(2L_0\). Which of the following statements provides the correct physical explanation for this observation?

A person stands at rest on a low-friction turntable that is free to rotate about a vertical axis, holding a bicycle wheel that is spinning rapidly about a vertical axle with angular momentum of magnitude \(L_0\) directed upward. When the person inverts the wheel upside down by \(180^\circ\) so that its angular momentum points downward with magnitude \(L_0\), the person and turntable begin rotating such that their angular momentum is directed upward with magnitude \(2L_0\). Which of the following statements provides the correct physical explanation for this observation?

![A two-panel grayscale diagram labeled Initial on the left and Final on the right. In the Initial panel, a simplified stick figure stands centered on a horizontal circular platform mounted to a vertical support rod. The figure holds a horizontal bicycle wheel by its vertical axle; a vertical arrow labeled L_0 points straight upward from the wheel center. In the Final panel, the figure remains standing on the circular platform holding the bicycle wheel, but the axle is inverted; a vertical arrow labeled L_0 points straight downward from the wheel center. A curved arrow on the circular platform indicates counterclockwise rotation, with a vertical arrow labeled 2L_0 pointing straight upward from the platform axle. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604266-53UpSi.jpg)

- **A.** Because there is no net external torque acting along the vertical axis, the total vertical angular momentum must remain conserved at \(+L_0\); when the wheel's vector changes by \(-2L_0\) from \(+L_0\) to \(-L_0\), the turntable must acquire \(+2L_0\) to keep the total constant.
- **B.** The muscular torque exerted by the person to invert the wheel acts as an external torque on the system, which delivers a vertical angular impulse of \(+2L_0\) that sets the turntable into rotational motion.
- **C.** Because the turntable was initially at rest, the total vertical angular momentum of the system must remain zero at all times, requiring the turntable to rotate with \(+2L_0\) to counteract both the initial and final states of the wheel.
- **D.** Because the spin speed of the wheel remains constant, the wheel's angular momentum magnitude is unchanged, meaning the turntable rotates because mechanical work done during the flip converts internal energy into rotational momentum.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124241/*