A solid sphere of mass M and radius R is rotating about an axis through its center. What is its moment of inertia?
Correct Answer: I = 2/5 MR^2
- Step 1: Understand what moment of inertia means. It is a measure of how difficult it is to change the rotation of an object.
- Step 2: Identify the shape of the object. In this case, it is a solid sphere.
- Step 3: Know the formula for the moment of inertia of a solid sphere. It is I = 2/5 MR^2.
- Step 4: Recognize the variables in the formula: M is the mass of the sphere, and R is the radius of the sphere.
- Step 5: Substitute the values of M and R into the formula if you have them, or use the formula as is to express the moment of inertia.
- Moment of Inertia – The moment of inertia is a measure of an object's resistance to changes in its rotation about an axis.
- Solid Sphere Properties – Understanding the specific formula for the moment of inertia of a solid sphere, which is derived from its mass distribution.
- Rotational Dynamics – The relationship between mass, radius, and rotational motion, particularly how they affect the moment of inertia.
