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title: "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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url: "https://nerd-notes.com/ubq/124459/"
date_modified: "2026-09-28T14:05:40+00:00"
---

# 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 \(a_{t,A}\)?

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 \(a_{t,A}\)?

![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.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604340-WnDx2H.jpg)

- **A.** Angular speed: \(\omega_B = \dfrac{1}{2}\omega_A\) ; Tangential acceleration: \(a_{t,B} = 2a_{t,A}\)
- **B.** Angular speed: \(\omega_B = \dfrac{1}{2}\omega_A\) ; Tangential acceleration: \(a_{t,B} = a_{t,A}\)
- **C.** Angular speed: \(\omega_B = 2\omega_A\) ; Tangential acceleration: \(a_{t,B} = 2a_{t,A}\)
- **D.** Angular speed: \(\omega_B = 2\omega_A\) ; Tangential acceleration: \(a_{t,B} = a_{t,A}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124459/*