---
title: "A car of mass \\( M \\) moves around a circularly banked curve on a freeway off-ramp. The off-ramp has a radius of curvature \\( R \\) and is raised to an angle \\( \\theta \\) from the horizontal. The road is slick, and friction is negligible."
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url: "https://nerd-notes.com/ubq/81479/"
date_modified: "2025-12-26T11:16:15+00:00"
---

# A car of mass \( M \) moves around a circularly banked curve on a freeway off-ramp. The off-ramp has a radius of curvature \( R \) and is raised to an angle \( \theta \) from the horizontal. The road is slick, and friction is negligible.

A car of mass \( M \) moves around a circularly banked curve on a freeway off-ramp. The off-ramp has a radius of curvature \( R \) and is raised to an angle \( \theta \) from the horizontal. The road is slick, and friction is negligible.

**Part a)** Draw a free body diagram showing all real forces acting on the car as it moves around the circular off-ramp. Clearly indicate a coordinate system in your diagram. *(3 points)*

**Part b)** Derive an expression for the speed of the car as it moves around the circular path. Your answer should be in terms of \( M, R, \theta \) and physical constants as appropriate. *(3 points)*

**Part c)** Calculate the speed of the car as it moves around the banked curve given \( \theta = 20.0^\circ \), \( M = 1150 \; \text{kg} \), \( R = 30.0 \; \text{m} \). *(3 points)*


*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/81479/*