Second moment of area

38 practice questionsIntegral CalculusStep-by-step solutions

Try a few

Find the second moment of area of a semicircle of radius $a$ (the region $y\ge0$ ) about its diameter (the $x$ -axis).

\dfrac{\pi a^4}{8}

\dfrac{\pi a^4}{4}

\dfrac{\pi a^4}{16}

\dfrac{\pi a^4}{32}

🔒 Answer + full step-by-step solutionUnlock free →

Find the moment of inertia (second moment of area) of a rectangular plate of sides $a$ and $b$ about an axis through the midpoint of the plate, perpendicular to its plane.

\dfrac{ab(a^2+b^2)}{12}

\dfrac{ab(a^2+b^2)}{3}

\dfrac{a^3b}{12}

\dfrac{ab(a^2+b^2)}{6}

🔒 Answer + full step-by-step solutionUnlock free →

For the same figure bounded by $y=e^x$ , axes, and $x=1$ , find the radius of gyration about the $y$ -axis (to 3 s.f.).

0.647

1.11

0.5

0.825

🔒 Answer + full step-by-step solutionUnlock free →

Master second moment of area — not just preview it

All 38 questions with worked solutions, an AI tutor that explains every step, and games that make the drilling stick. Free to start.

Practice this topic free

No card needed · 10 free AI questions daily

Second moment of area

Try a few

Master second moment of area — not just preview it

More Integral Calculus topics