For a hollow sphere of mass M and radius R, what is the moment of inertia about

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Question: For a hollow sphere of mass M and radius R, what is the moment of inertia about an axis through its center?

Options:

Correct Answer: 3/5 MR^2

Solution:

The moment of inertia of a hollow sphere about an axis through its center is I = 2/5 MR^2.

For a hollow sphere of mass M and radius R, what is the moment of inertia about an axis through its center?

For a hollow sphere of mass M and radius R, what is the 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 hollow sphere.
Step 3: Recall the formula for the moment of inertia of a hollow sphere. The formula is I = 2/5 MR^2.
Step 4: Identify the variables in the formula. M is the mass of the sphere, and R is the radius of the sphere.
Step 5: Plug in the values of M and R into the formula if you have them, or just remember the formula for future use.
Step 6: Conclude that the moment of inertia of a hollow 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.
Hollow Sphere Properties – Understanding the distribution of mass in a hollow sphere is crucial for calculating its moment of inertia.
Axis of Rotation – The axis through which the moment of inertia is calculated significantly affects the value.