---
title: "A particle of mass \\(m\\) moves in a horizontal circular path of radius \\(R\\) on a frictionless surface. The particle speeds up over time such that its tangential speed \\(v(t)\\) increases continuously. At a given instant, the net force acting on the particle has a radial component of magnitude \\(F_{\\text{rad}}\\) directed toward the center of the path and a tangential component of magnitude \\(F_{\\text{tan}}\\) in the direction of motion. Which of the following correctly identifies the instantaneous power \\(P_{\\text{rad}}\\) delivered to the particle by the radial component and correctly relates the instantaneous power \\(P_{\\text{tan}}\\) delivered by the tangential component to the total instantaneous power \\(P_{\\text{net}}\\) delivered to the particle?"
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/124112/"
date_modified: "2026-09-28T13:30:28+00:00"
---

# A particle of mass \(m\) moves in a horizontal circular path of radius \(R\) on a frictionless surface. The particle speeds up over time such that its tangential speed \(v(t)\) increases continuously. At a given instant, the net force acting on the particle has a radial component of magnitude \(F_{\text{rad}}\) directed toward the center of the path and a tangential component of magnitude \(F_{\text{tan}}\) in the direction of motion. Which of the following correctly identifies the instantaneous power \(P_{\text{rad}}\) delivered to the particle by the radial component and correctly relates the instantaneous power \(P_{\text{tan}}\) delivered by the tangential component to the total instantaneous power \(P_{\text{net}}\) delivered to the particle?

A particle of mass \(m\) moves in a horizontal circular path of radius \(R\) on a frictionless surface. The particle speeds up over time such that its tangential speed \(v(t)\) increases continuously. At a given instant, the net force acting on the particle has a radial component of magnitude \(F_{\text{rad}}\) directed toward the center of the path and a tangential component of magnitude \(F_{\text{tan}}\) in the direction of motion. Which of the following correctly identifies the instantaneous power \(P_{\text{rad}}\) delivered to the particle by the radial component and correctly relates the instantaneous power \(P_{\text{tan}}\) delivered by the tangential component to the total instantaneous power \(P_{\text{net}}\) delivered to the particle?

![An overhead schematic view of a horizontal circular path of radius R shown as a thin dashed circle. At the rightmost point of the circular path, a small filled solid circular dot represents the particle of mass m. Directed vertically upward from the dot is a solid straight arrow labeled v with an arrowhead at its top end, tangent to the circular path. Directed horizontally to the left from the dot toward the center of the circular path is a solid straight arrow labeled F_{\text{rad}} with an arrowhead at the left end. Directed vertically upward from the dot, collinear with and parallel to the velocity arrow, is a second solid straight arrow labeled F_{\text{tan}} with an arrowhead at its top end. A plus sign inside a small circle marks the geometric center of the circular path. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790602228-qCAneZ.jpg)

- **A.** \(P_{\text{rad}} = 0\) ; \(P_{\text{tan}} = P_{\text{net}}\)
- **B.** \(P_{\text{rad}} = 0\) ; \(P_{\text{tan}} < P_{\text{net}}\)
- **C.** \(P_{\text{rad}} > 0\) ; \(P_{\text{tan}} = P_{\text{net}}\)
- **D.** \(P_{\text{rad}} > 0\) ; \(P_{\text{tan}} < P_{\text{net}}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124112/*