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AP Physics C: Mechanics
5.4 Rotational Inertia
IntermediateMCQConceptual24.2k
An irregularly shaped two-dimensional enclosed outline representing a rigid body of mass \(M\). Inside the outline, a small solid dot labeled \(\text{CM}\) marks the center of mass. A dashed vertical line passes through \(\text{CM}\). To the left of \(\text{CM}\), a small solid dot labeled \(A\) marks axis \(A\), with a parallel vertical dashed line passing through it. A horizontal double-headed arrow between axis \(A\) and \(\text{CM}\) is labeled \(d_A\). To the right of \(\text{CM}\), a small solid dot labeled \(B\) marks axis \(B\), with a parallel vertical dashed line passing through it. A horizontal double-headed arrow between \(\text{CM}\) and axis \(B\) is labeled \(d_B\). A horizontal double-headed arrow spanning directly from axis \(A\) to axis \(B\) is labeled \(d\). No other labels, lines, text, or axes appear.
A rigid body with center of mass CM and two parallel axes A and B.
A student calculates the rotational inertia \(I_A\) of a rigid body of mass \(M\) about an axis \(A\) located a distance \(d_A\) from the center of mass. To determine the rotational inertia \(I_B\) about a parallel axis \(B\) located a distance \(d\) from axis \(A\) and \(d_B\) from the center of mass, the student uses the relation \(I_B = I_A + M d^2\). This calculation yields an incorrect value for \(I_B\). Which of the following best explains why the student's calculation is incorrect and how the correct value of \(I_B\) must be found?

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