---
title: "A rigid baton consists of a thin, uniform rod of length \\(L\\) and mass \\(M\\). A small, solid sphere, also of mass \\(M\\), is securely attached to the right end of the rod, labeled End A. The left end of the rod is labeled End B. The center of mass of the baton is located at a distance of \\(L/4\\) from End A, and is marked with an ‘X’, as shown in Figure 1.  In Experiment 1, the baton is tossed into the air such that it moves in a vertical plane, spinning clockwise as it travels in a parabolic trajectory. Air resistance is negligible."
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url: "https://nerd-notes.com/ubq/110391/"
date_modified: "2026-04-02T05:19:27+00:00"
---

# A rigid baton consists of a thin, uniform rod of length \(L\) and mass \(M\). A small, solid sphere, also of mass \(M\), is securely attached to the right end of the rod, labeled End A. The left end of the rod is labeled End B. The center of mass of the baton is located at a distance of \(L/4\) from End A, and is marked with an ‘X’, as shown in Figure 1.

In Experiment 1, the baton is tossed into the air such that it moves in a vertical plane, spinning clockwise as it travels in a parabolic trajectory. Air resistance is negligible.

A rigid baton consists of a thin, uniform rod of length \(L\) and mass \(M\). A small, solid sphere, also of mass \(M\), is securely attached to the right end of the rod, labeled End A. The left end of the rod is labeled End B. The center of mass of the baton is located at a distance of \(L/4\) from End A, and is marked with an 'X', as shown in Figure 1.

In Experiment 1, the baton is tossed into the air such that it moves in a vertical plane, spinning clockwise as it travels in a parabolic trajectory. Air resistance is negligible.

![A horizontal uniform rod. The right end is labeled 'End A' and has a small shaded sphere attached to it. The left end is labeled 'End B'. A clear 'X' mark is on the rod, closer to End A. A horizontal dimension line above the rod indicates the length of the entire rod is L. Another dimension line below the rod indicates the distance from End A to the 'X' is L/4.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1775107164-KRojnE.jpg)

**Part a)** A student observes the baton in flight and claims: 'As the baton moves upward, the downward force of gravity creates a torque that causes the baton\'s spin to slow down.' **Explain** why the student\'s claim is incorrect using physical principles. *(3 points)*

**Part b)** The baton rotates clockwise as it travels through the air. Let the counterclockwise direction be positive. *(3 points)*

**Part c)** Figure 2 shows the baton at the instant it is released. The baton is moving upward and to the right while rotating clockwise. On Figure 2, **sketch** the trajectory of the center of mass (the 'X') from the moment of release until it reaches its maximum height. On the same figure, **sketch** the trajectory of End B for the same time interval. *(2 points)*

**Part d)** In Experiment 2, the baton is mounted on a fixed, vertical, frictionless axle that passes exactly through its center of mass (the 'X'). The baton rests on a horizontal table. Starting at time \(t=0\), a student applies a constant horizontal force of magnitude \(F_0\) to End B. The force is always directed perpendicular to the rod, causing the baton to rotate. Let the direction of the baton\'s rotation be positive. *(4 points)*


*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/110391/*