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AP Physics C: Mechanics
5.2 Connecting Linear and Rotational Motion
5.1 Rotational Kinematics
IntermediateMCQMathematicalProportional AnalysisConceptual19.9k
A side-view diagram showing two circular cylinders, labeled A and B, mounted on parallel horizontal axles. Cylinder A, on the left, is larger with a radius labeled \(2R\), indicated by a dashed line segment extending from its center axle to its top rim. Cylinder B, on the right, is smaller with a radius labeled \(R\), indicated by a dashed line segment extending from its center axle to its top rim. A closed loop representing a belt wraps tightly around the outer rims of both cylinders, with straight horizontal upper and lower segments connecting them. A curved arrow near Cylinder A indicates clockwise rotation and is labeled \(\alpha_A\). A solid black dot on the rim of Cylinder A is labeled \(a_{t,A}\), and a solid black dot on the rim of Cylinder B is labeled \(a_{t,B}\). No other labels, lines, text, or axes appear.
Cylinders A and B of radii \(2R\) and \(R\) connected by an inextensible belt.
Two uniform cylinders, Cylinder A of radius \(2R\) and Cylinder B of radius \(R\), are mounted on separate, parallel, frictionless fixed axles and connected by a light belt that does not slip on either cylinder. Cylinder A is driven so that its angular speed \(\omega_A\) increases at a constant rate with angular acceleration \(\alpha_A\). Which of the following pairs correctly relates the angular speed \(\omega_B\) of Cylinder B to \(\omega_A\), and the magnitude of the tangential acceleration \(a_{t,B}\) of a point on the rim of Cylinder B to \(a_{t,A}\)?

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