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AP Physics 1
6.1 Rotational Kinetic Energy
5.4 Rotational Inertia
3.4 Conservation of Energy
Multi-Unit
AdvancedMCQMathematicalConceptual19.2k
A vertical view of a cylinder hanging from a ceiling. A thin line representing a string is fixed to the ceiling and extends downward, wrapping around the left side of a gray solid cylinder. The cylinder is shown at two positions: an initial top position and a lower position labeled with a downward arrow of length h pointing to the center of the cylinder. A radius R is drawn from the center of the cylinder to its edge.
A solid cylinder unwinding from a fixed string as it falls.
A uniform solid cylinder of mass \(M\) and radius \(R\) has a light string wrapped multiple times around its circumference. The free end of the string is attached to a fixed horizontal ceiling. The cylinder is held at rest and then released, falling vertically as the string unwinds without slipping. The rotational inertia of a solid cylinder about its center of mass is \(I = \dfrac{1}{2}MR^2\). After the center of mass of the cylinder has fallen a vertical distance \(h\), what is the speed of the center of mass of the cylinder?

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