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Center of Mass: Support Sheet

AP Physics C: Mechanics · Topic 2.1 · 4 levels · 24 questions · untimed

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This is a Support Sheet, not homework. It is not marked, not collected and not on the gradebook. Use it to check that you can set up \(\displaystyle x_{cm} = \frac{1}{M}\int x\,dm\) with \(dm = \lambda\,dx\) for a rod. Start at the level you need; stop when a level says secure. Nothing you do here is saved or sent anywhere.

Choose an answer, then press Check. You get the correct answer, why each wrong option is wrong, and the full working. Three error types are built into the wrong options: pulling \(\lambda(x)\) outside the integral, forgetting to divide by \(M\), and putting \(x_{cm}\) at \(L/2\) by reflex. Symbols: \(M\) total mass, \(\lambda\) linear density, \(dm\) mass element, \(x_{cm}\) center of mass. \(g = 10\) m/s².

Score: 0 / 24 · checked: 0

Sources: AP Physics C: Mechanics Course and Exam Description, Topic 2.1 (EK 2.1.B.1–2.1.B.4); released free-response questions 2021 (Q3), 2024 (Set 1 and Set 2) and 2026. g = 10 m/s² throughout.