AP Physics C: Mechanics
5.2 Connecting Linear and Rotational Motion
5.1 Rotational Kinematics
A flat circular turntable rotates about a fixed vertical axis passing perpendicularly through its center. Starting from rest at time \(t = 0\), the turntable experiences a time-dependent angular acceleration given by \(\alpha(t) = bt^2\), where \(b = 9.0\text{ rad/s}^4\). Three small markers, \(A\), \(B\), and \(C\), are placed on the turntable at the radial distances and observed at the times specified in the table below.
Which of the following correctly ranks the magnitudes of the total linear acceleration \(a\) of the three markers at their respective times of observation?
| Marker | Distance from Axis (\(r\)) | Time of Observation (\(t\)) |
|---|---|---|
| \(A\) | \(0.60\text{ m}\) | \(1.0\text{ s}\) |
| \(B\) | \(0.20\text{ m}\) | \(1.0\text{ s}\) |
| \(C\) | \(0.010\text{ m}\) | \(2.0\text{ s}\) |
Which of the following correctly ranks the magnitudes of the total linear acceleration \(a\) of the three markers at their respective times of observation?
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