All questions
AP Physics C: Mechanics
5.4 Rotational Inertia
IntermediateMCQMathematical17.6k
A horizontal dashed line represents the axis of rotation. Resting on this horizontal line is a semicircular curved line of radius \(R\) centered at an origin point indicated by a small solid dot on the horizontal line. The semicircle curves upward into the upper half-plane, with its left endpoint and right endpoint touching the horizontal dashed line at distances \(R\) from the center dot. A straight solid line segment extends from the center dot to a point on the semicircle at an angle \(\theta\) above the right side of the horizontal line, with an arc labeled \(\theta\) indicating this angle. The straight line segment has length labeled \(R\). A small arc segment of the wire at this position is shaded dark gray to represent a mass element \(dm\). No other labels, lines, text, or axes appear.
Semicircular wire with axis of rotation passing through its endpoints.
A thin, uniform wire of radius \(R\) and linear mass density \(\lambda\) is bent into a semicircle. An axis of rotation lies in the plane of the wire and passes through both endpoints of the semicircle. The angle \(\theta\) is measured from the axis of rotation to a segment of the wire, as shown. Which of the following integrals correctly represents the rotational inertia of the wire about this axis?

Log In to Continue

Accounts are free! Log in to try this question, see explanations, save progress, and more!

Similar Questions

Tools for a 5

The Quiz Lab library of AP Physics quizzes AP aligned mock tests to help you get a 5. With grading, adaptive explanations, and more. Find a Quiz Find, solve, and grade every AP FRQ ever. Find an FRQ Stuck on AP Physics C: Mechanics? Get unstuck with an AP specialist.1 to 1 tutors who know the exam inside out. Understand weeks of material in a single session.Find a Tutor Learn AP Physics from scratch, quickly. This is the only course you'll need for the year. A self-paced course with everything you need to get a 5. Trusted by over 15,000 students and 200+ schools. Learn fast, or we'll refund your purchase, backed by our 100% satisfaction guarantee. Explore the Course