(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A mass distribution in the positive x region of the xy-plane and in the shape of a semicircle of radius a, centred on the origin, has mass per unit area k. Find, using plane polar coordinates, its moments of inertia about the x and y axes.

2. Relevant equations

3. The attempt at a solution

I know that I=∫r^2.dm

dm=k.dA=k.r.dr.dθ in polar coordinates.

So I=k∫dθ∫r^3.dr

But I'm not sure about the limits, or how to differentiate between the moments of inertia about the x and y axes.

Any help would be brilliant.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Moments of inertia by integration

**Physics Forums | Science Articles, Homework Help, Discussion**