Question: If a solid sphere of radius R and mass M is rotating about an axis through its center, what is its moment of inertia?
Options:
2/5 MR^2
3/5 MR^2
1/2 MR^2
1/3 MR^2
Correct Answer: 2/5 MR^2
Solution:
The moment of inertia of a solid sphere about its center is I = 2/5 MR^2.
If a solid sphere of radius R and mass M is rotating about an axis through its c
Practice Questions
Q1
If a solid sphere of radius R and mass M is rotating about an axis through its center, what is its moment of inertia?
2/5 MR^2
3/5 MR^2
1/2 MR^2
1/3 MR^2
Questions & Step-by-Step Solutions
If a solid sphere of radius R and mass M is rotating about an axis through its center, what is its moment of inertia?
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 that 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 just remember the formula for future use.
Moment of Inertia – The moment of inertia is a measure of an object's resistance to changes in its rotation, depending on the mass distribution relative to the axis of rotation.
Solid Sphere Properties – Understanding the specific formula for the moment of inertia of a solid sphere, which is derived from its mass and radius.
Rotational Dynamics – The principles governing the motion of rotating bodies and how mass distribution affects rotational motion.
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