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title: "A rigid horizontal turntable rotates about a fixed, frictionless vertical axis through its center. While the turntable is rotating with angular speed \\(\\omega\\), a constant braking torque is applied, producing an angular acceleration \\(\\alpha\\) that steadily brings the turntable to rest. A student hypothesizes that at some instant before the turntable stops, the deceleration will cancel the inward acceleration, causing the net linear acceleration of a point on the rim to become zero. However, an accelerometer mounted at a fixed distance \\(r > 0\\) from the axis measures a non-zero net linear acceleration at all times until rotation ceases. Which of the following statements provides the correct physical explanation for this observation?"
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url: "https://nerd-notes.com/ubq/124230/"
date_modified: "2026-09-28T14:04:21+00:00"
---

# A rigid horizontal turntable rotates about a fixed, frictionless vertical axis through its center. While the turntable is rotating with angular speed \(\omega\), a constant braking torque is applied, producing an angular acceleration \(\alpha\) that steadily brings the turntable to rest. A student hypothesizes that at some instant before the turntable stops, the deceleration will cancel the inward acceleration, causing the net linear acceleration of a point on the rim to become zero. However, an accelerometer mounted at a fixed distance \(r > 0\) from the axis measures a non-zero net linear acceleration at all times until rotation ceases. Which of the following statements provides the correct physical explanation for this observation?

A rigid horizontal turntable rotates about a fixed, frictionless vertical axis through its center. While the turntable is rotating with angular speed \(\omega\), a constant braking torque is applied, producing an angular acceleration \(\alpha\) that steadily brings the turntable to rest. A student hypothesizes that at some instant before the turntable stops, the deceleration will cancel the inward acceleration, causing the net linear acceleration of a point on the rim to become zero. However, an accelerometer mounted at a fixed distance \(r > 0\) from the axis measures a non-zero net linear acceleration at all times until rotation ceases. Which of the following statements provides the correct physical explanation for this observation?

- **A.** The tangential and radial accelerations act along the same radial line in opposite directions, but the magnitude of the tangential acceleration remains strictly smaller than the radial acceleration until the turntable comes to a complete stop.
- **B.** The centripetal acceleration is an apparent effect that exists only in a rotating reference frame, so the accelerometer detects only the tangential acceleration, which is maintained at a constant non-zero value by the braking torque.
- **C.** The net linear acceleration is the vector sum of perpendicular radial and tangential components, whose magnitude \(\sqrt{(r\omega^2)^2 + (r\alpha)^2}\) cannot vanish because the radial term \(r\omega^2\) remains non-zero as long as the angular speed is non-zero.
- **D.** The continuous removal of mechanical energy by the braking torque requires the net linear force on the accelerometer to oppose its instantaneous displacement, meaning the acceleration must remain entirely tangential throughout the slowing process.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124230/*