---
title: "A small ball of mass \\(m\\) moves horizontally with speed \\(v\\) toward a uniform thin rod of mass \\(M\\) and length \\(L\\) that is hanging vertically from a frictionless pivot attached to the ceiling. The ball strikes the bottom end of the rod and sticks to it. During the collision, the ball-rod system is analyzed.  Which of the following correctly describes the conservation of linear momentum and the conservation of angular momentum about the pivot for the ball-rod system during the collision?"
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url: "https://nerd-notes.com/ubq/112720/"
date_modified: "2026-04-30T21:07:06+00:00"
---

# A small ball of mass \(m\) moves horizontally with speed \(v\) toward a uniform thin rod of mass \(M\) and length \(L\) that is hanging vertically from a frictionless pivot attached to the ceiling. The ball strikes the bottom end of the rod and sticks to it. During the collision, the ball-rod system is analyzed.

Which of the following correctly describes the conservation of linear momentum and the conservation of angular momentum about the pivot for the ball-rod system during the collision?

A small ball of mass \(m\) moves horizontally with speed \(v\) toward a uniform thin rod of mass \(M\) and length \(L\) that is hanging vertically from a frictionless pivot attached to the ceiling. The ball strikes the bottom end of the rod and sticks to it. During the collision, the ball-rod system is analyzed.

Which of the following correctly describes the conservation of linear momentum and the conservation of angular momentum about the pivot for the ball-rod system during the collision?

![A vertical rod is hanging from a pivot on the ceiling. A small ball is shown moving horizontally toward the bottom end of the rod with a velocity vector labeled v. An axis of rotation is indicated at the pivot point at the top of the rod.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1777583226-err1Nz.jpg)

- **A.** Both linear momentum and angular momentum are conserved because the forces involved in the collision are internal to the ball-rod system.
- **B.** Linear momentum is conserved because the collision is instantaneous, but angular momentum is not conserved because the pivot exerts an external force.
- **C.** Angular momentum is conserved because the pivot force exerts no torque about the pivot axis, but linear momentum is not conserved because the pivot exerts an external force on the system.
- **D.** Neither linear momentum nor angular momentum is conserved because the collision is inelastic and the pivot is an external constraint.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/112720/*