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AP Physics C: Mechanics
6.5 Rolling
AdvancedMCQDrawing RepresentationsConceptual22.2k
A side-view schematic diagram of a circular spool resting on a flat horizontal floor. An outer solid circle of radius \(R\) touches a horizontal ground line at a single contact point at the very bottom. A smaller, concentric dashed circle of radius \(r\) is centered at the same midpoint, marked with a solid dot labeled \(O\). A straight solid arrow extends from center \(O\) upward to the rim of the outer circle, labeled \(R\). A second straight solid arrow extends from center \(O\) upward to the rim of the inner dashed circle, labeled \(r\). A horizontal line representing a string is wrapped under the inner dashed circle and extends horizontally to the right from the lowest point of the inner dashed circle, located at distance \(r\) directly below \(O\). At the right end of this horizontal string, an arrow points to the right and is labeled \(\vec{T}\). No other labels, lines, text, or axes appear.
Spool resting on a horizontal floor with string pulled horizontally from the bottom of the inner hub.
A spool of total mass \(M\), outer radius \(R\), and rotational inertia \(I\) about its central axis rests on a rough horizontal surface.

A light string wrapped around an inner hub of radius \(r\) (where \(r < R\)) is pulled horizontally to the right with a constant tension \(\vec{T}\) such that the string unwinds from the bottom of the hub, a distance \(r\) below the central axis. The spool rolls without slipping along the surface. Which of the following extended free-body diagrams best represents the forces acting on the spool and their relative magnitudes?

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