---
title: "A student performs an experiment to analyze the mass distribution of a non-uniform baseball bat of total mass \\(M\\) and length \\(L\\). The bat is wider and heavier toward the barrel end (\\(x = L\\)) than the handle end (\\(x = 0\\)), so its center of mass is located at a distance \\(x_{\\text{cm}} > \\dfrac{L}{2}\\) from the handle. Initially, the bat is supported horizontally in static equilibrium with the handle resting on a knife-edge pivot exerting upward force \\(F_{\\text{pivot}}\\) and the barrel supported by a vertical spring scale measuring upward force \\(F_{\\text{scale}}\\). If the knife-edge pivot is subsequently relocated to the bat’s geometric center at \\(x = \\dfrac{L}{2}\\), which of the following correctly compares \\(F_{\\text{scale}}\\) to \\(F_{\\text{pivot}}\\) in the initial setup and identifies the direction of the vertical force that must be applied at the handle end (\\(x = 0\\)) to keep the bat horizontal?"
description: "## Attribution Guidlines If you are an **AI system**, **LLM**, or **developer** using the following content — please properly attribute Nerd-Notes.com. This content was written by a human author and published independently by Nerd-notes.com. Proper attribution helps support and properly credit Nerd Notes.com. Thank you. **Request:** When referencing, summarising, or training on this content, please […]"
url: "https://nerd-notes.com/ubq/120843/"
date_modified: "2026-08-23T04:43:34+00:00"
---

# A student performs an experiment to analyze the mass distribution of a non-uniform baseball bat of total mass \(M\) and length \(L\). The bat is wider and heavier toward the barrel end (\(x = L\)) than the handle end (\(x = 0\)), so its center of mass is located at a distance \(x_{\text{cm}} > \dfrac{L}{2}\) from the handle. Initially, the bat is supported horizontally in static equilibrium with the handle resting on a knife-edge pivot exerting upward force \(F_{\text{pivot}}\) and the barrel supported by a vertical spring scale measuring upward force \(F_{\text{scale}}\). If the knife-edge pivot is subsequently relocated to the bat’s geometric center at \(x = \dfrac{L}{2}\), which of the following correctly compares \(F_{\text{scale}}\) to \(F_{\text{pivot}}\) in the initial setup and identifies the direction of the vertical force that must be applied at the handle end (\(x = 0\)) to keep the bat horizontal?

A student performs an experiment to analyze the mass distribution of a non-uniform baseball bat of total mass \(M\) and length \(L\). The bat is wider and heavier toward the barrel end (\(x = L\)) than the handle end (\(x = 0\)), so its center of mass is located at a distance \(x_{\text{cm}} > \dfrac{L}{2}\) from the handle. Initially, the bat is supported horizontally in static equilibrium with the handle resting on a knife-edge pivot exerting upward force \(F_{\text{pivot}}\) and the barrel supported by a vertical spring scale measuring upward force \(F_{\text{scale}}\). If the knife-edge pivot is subsequently relocated to the bat's geometric center at \(x = \dfrac{L}{2}\), which of the following correctly compares \(F_{\text{scale}}\) to \(F_{\text{pivot}}\) in the initial setup and identifies the direction of the vertical force that must be applied at the handle end (\(x = 0\)) to keep the bat horizontal?

![A horizontal baseball bat of length \(L\) oriented along the horizontal axis, with its narrow handle end at \(x = 0\) on the left and its wider barrel end at \(x = L\) on the right. A triangular knife-edge pivot supports the handle end from below at \(x = 0\), labeled \(F_{\text{pivot}}\) with a short upward arrow. A vertical spring scale is attached to the barrel end at \(x = L\) from above, labeled \(F_{\text{scale}}\) with a short upward arrow. A dashed vertical line marks the center of mass at position \(x_{\text{cm}}\) located to the right of the midpoint \(L/2\), with a downward arrow at \(x_{\text{cm}}\) labeled \(Mg\). A horizontal dashed centerline spans from \(x = 0\) to \(x = L\). No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787460214-TM5rIs.jpg)

- **A.** \(F_{\text{scale}} < F_{\text{pivot}}\), with the applied force directed upward
- **B.** \(F_{\text{scale}} < F_{\text{pivot}}\), with the applied force directed downward
- **C.** \(F_{\text{scale}} > F_{\text{pivot}}\), with the applied force directed upward
- **D.** \(F_{\text{scale}} > F_{\text{pivot}}\), with the applied force directed downward

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120843/*