How Do You Calculate the Moment of Inertia for a Uniform Solid Block?

[demonelite123]

a uniform solid block has mass 0.172 kg and edge lengths a=3.5cm, b=8.4cm, and c=1.4cm (c is the height of the rectangular solid).Calculate its rotational inertia about an axis through one corner and perpendicular to the large faces.

i know the formula is integral of r^2 dm, but i have no idea what to do here. i have r^2 = a^2 + b^2. but i don't know how what to substitute for dm.

 

[tiny-tim]

Hi demonelite123!

(try using the X² tag just above the Reply box )

i know the formula is integral of r^2 dm, but i have no idea what to do here. i have r^2 = a^2 + b^2. but i don't know how what to substitute for dm.

If r² = x² + y², then dm = density times dxdydz (or, if you're only integrating over x and y, then dm = hdxdy).