Moment of inertia of disk about off centre axis

[Lucy Yeats]

Homework Statement

Find the moment of inertia of a uniform disk of mass m and radius r about an axis normal to the disk, through a point x from the centre.

Homework Equations

The Attempt at a Solution

Let ρ be the density. I=ρ∫r^2 dA=ρ∫∫r^3 dr dθ in polar coordinates.
However I don't know what the limits of r should be. θ is between 0 and 2 pi, but r max varies, so I'm confused.

 

[andrien]

use parallel axis theorem

 

[ehild]

The Attempt at a Solution

Let ρ be the density. I=ρ∫r^2 dA=ρ∫∫r^3 dr dθ in polar coordinates.
However I don't know what the limits of r should be. θ is between 0 and 2 pi, but r max varies, so I'm confused.

Your integral is not correct.
The contribution to the moment of inertia of a mass element, at distance D from the axis, is D²dm. Write up D in terms of r and φ (the polar coordinates. ) You have to integrate for the whole disk.

ehild