Determine the moment of inertia of a solid sphere of mass M and radius R about a

Determine the moment of inertia of a solid sphere of mass M and radius R about an axis through its center.

Determine the moment of inertia of a solid sphere of mass M and radius R about an axis through its center.

Step 1: Understand what moment of inertia is. It measures how difficult it is to rotate an object around an axis.
Step 2: Identify the shape of the object. In this case, we have a solid sphere.
Step 3: Know the formula for the moment of inertia of a solid sphere. It is I = 2/5 MR^2, where M is the mass and R is the radius.
Step 4: Substitute the values of mass (M) and radius (R) into the formula if needed, but the formula itself gives the moment of inertia directly.
Step 5: Conclude that the moment of inertia of a solid sphere about an axis through its center is I = 2/5 MR^2.

Moment of Inertia – The moment of inertia is a measure of an object's resistance to rotational motion about a given axis.
Solid Sphere Properties – Understanding the distribution of mass in a solid sphere is crucial for calculating its moment of inertia.
Integration in Physics – The calculation often involves integrating over the volume of the sphere to account for the mass distribution.