The Perpendicular Axis Theorem says that the moment of inertia of a flat, planar

Question

The Perpendicular Axis Theorem says that the moment of inertia of a flat, planar object about any axis is the SUM of the moments of inertia of the ob ject about two other mutually perpendicular axis, all of which have the same origin. Use this theorem (and a moment of inertia that you already know!) to find the moment of inertia of a flat disk of mass M and radius R spun about an axis going through the center of the disk and lying 111 the plane of the disk. Then do the integral to find the moment of inertia directly and see if you get the same answer!

Explanation / Answer

Moment of Inertia of the disk about and axis passing through center of mass and

perpendicular to the plane of the disk,

Iz = M*R^2/2

let Ix and IY are Moments of Inertia of the disk about two axis passing through center of mass

and parallel to the plane of the disk. And these two axis are peprpendicular to each other.

According Perpendicular axis theorem,

Iz = Ix + Iy

IZ = Ix + Ix (since IY = Ix)

Iz = 2*Ix

Ix = Iz/2

= (M*R^2/2)/2

= M*R^2/4 <<<<<<<<<<<-------------------Answer

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