A solid sphere of mass M and radius R is rolling without slipping. What is its m

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Question: A solid sphere of mass M and radius R is rolling without slipping. What is its moment of inertia about an axis through its center?

Options:

Correct Answer: 2/5 MR^2

Solution:

The moment of inertia of a solid sphere about its center is I = 2/5 MR^2.

A solid sphere of mass M and radius R is rolling without slipping. What is its moment of inertia about an axis through its center?

A solid sphere of mass M and radius R is rolling without slipping. What is its moment of inertia about an axis through its center?

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: Recall the formula for the moment of inertia of a solid sphere about its center. The formula 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 they are given, 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, depending on the mass distribution relative to the axis of rotation.
Rolling Motion – Rolling without slipping involves both translational and rotational motion, where the point of contact with the ground does not slide.