a solid disk of mass m and radius r

A solid disk of mass m and radius r is a three-dimensional object that has a circular shape and a uniform thickness throughout its structure. It can be modeled as a two-dimensional disk with mass uniformly distributed across its surface, which makes it a homogeneous object. The moment of inertia of a solid disk of mass m and radius r about an axis perpendicular to its surface and passing through its center is given by:

I = (1/2)mr^2

where I is the moment of inertia and m and r are the mass and radius of the disk, respectively. This moment of inertia represents the disk's resistance to rotational motion and depends on its mass distribution and the distance of the mass from the axis of rotation. The moment of inertia of a solid disk is a commonly used example in physics problems and is often used to explain concepts related to rotational motion and angular momentum.