For a given mass, which of the following configurations will have the smallest m

₹0.0

Question: For a given mass, which of the following configurations will have the smallest moment of inertia?

Options:

Correct Answer: All mass at the center

Solution:

The moment of inertia is smallest when all mass is concentrated at the center, as it minimizes the distance from the axis of rotation.

For a given mass, which of the following configurations will have the smallest moment of inertia?

For a given mass, which of the following configurations will have the smallest moment of inertia?

Step 1: Understand what moment of inertia means. It is a measure of how difficult it is to rotate an object around an axis.
Step 2: Recognize that the moment of inertia depends on how mass is distributed relative to the axis of rotation.
Step 3: Know that the farther the mass is from the axis, the larger the moment of inertia will be.
Step 4: Realize that if all the mass is concentrated at the center, it is closest to the axis of rotation.
Step 5: Conclude that having all mass at the center minimizes the distance from the axis, resulting in the smallest moment of inertia.

Moment of Inertia – The moment of inertia quantifies how mass is distributed relative to an axis of rotation, affecting rotational motion.
Axis of Rotation – The line about which an object rotates, which influences the moment of inertia based on the distribution of mass.
Mass Distribution – The arrangement of mass in relation to the axis of rotation, where closer mass results in a lower moment of inertia.