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AP Physics C: Mechanics
5.4 Rotational Inertia
AdvancedMCQMathematical23.9k
A set of perpendicular coordinate axes labeled x horizontally and y vertically, intersecting at an origin labeled O. In the upper half-plane, a thick solid semicircular arc of radius R is centered at the origin, extending from the negative x-axis at (-R, 0) through the positive y-axis at (0, R) to the positive x-axis at (R, 0). A single straight dashed arrow extends from the origin O to a point on the arc at an angle in the first quadrant, labeled R. A filled circle sits on the positive y-axis between the origin and the top of the arc, labeled CM. No other labels, lines, text, or axes appear.
A uniform semicircular wire of radius R in the xy-plane.
A thin, uniform wire of total mass \(M\) and radius \(R\) is bent into a semicircle and lies in the \(xy\)-plane, centered symmetrically about the \(y\)-axis with its center of curvature at the origin. What is the rotational inertia of the wire about an axis perpendicular to the \(xy\)-plane that passes through the center of mass of the wire?

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