head turn?

$4.$ Let's come back to these structures $-$ but no worries, no integrals needed this time if you don't want to$!$ The idea is to find the moment of inertia of each one of them around an axis that goes through one of their ends.

A$.$ A thin L square $-$ two straight edges held together at right angles. Each has length $a,$ and the total mass of the pair is $M.$

B$.$ A thin bar bent into a semicircle of radius a and total mass $M.$

One way of thinking about this is imagining you have them on a table, lying flat, and you can rotate them around one of the ends, similarly to the animation shown. Technically, you want to calculate $I={\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}dm{r}^2.$ If you feel comfortable with calculus, go for it$!($Warning$!$ The integral in part B might be very hard!$)$ But it's totally okay if you don't. You can divide each structure into little chunks, each chunk of the same mass $m$ and at a respective distance $r_i$ to the axis of rotation, and you can calculate the sum $I=m_i{r}_i^2$ to get a really good approximation of its moment of inertia! Try using numbers for a and $M$ if that makes it easier for you. Start with $5$ or $10$ chunks. Next week we're going to see a way to calculate this