How does mass distribution affect an object's moment of inertia during rotation?

How does mass distribution affect an object's moment of inertia during rotation?

• A. It decreases with mass near the axis
• B. It remains constant regardless of mass
• C. It increases with mass farther from the axis
• D. It only affects the rotational speed

Answer: (C)

The moment of inertia of an object is a measure of how its mass is distributed with respect to the axis of rotation. Specifically, it reflects how difficult it is to change the object's rotational motion. When mass is distributed farther from the axis of rotation, the moment of inertia increases. This is because the moment of inertia is calculated as the sum of the products of each mass element and the square of its distance from the axis of rotation. Therefore, as more mass is located further away from the rotation axis, the moment of inertia gets larger. For the chosen answer, as an object's mass increases and is positioned farther away from the axis of rotation, each mass element contributes more significantly to the overall moment of inertia. This means that for the same amount of rotational force (torque), the object will experience a smaller angular acceleration than it would if more mass were concentrated closer to the axis. In contrast, the other choices do not accurately capture the relationship between mass distribution and moment of inertia. Mass located near the axis does not decrease the moment of inertia; rather, it contributes less to it. The moment of inertia is not a constant value as mass is added or changed; it is directly influenced by how that mass is distributed relative to the rotation axis

The moment of inertia of an object is a measure of how its mass is distributed with respect to the axis of rotation. Specifically, it reflects how difficult it is to change the object's rotational motion. When mass is distributed farther from the axis of rotation, the moment of inertia increases. This is because the moment of inertia is calculated as the sum of the products of each mass element and the square of its distance from the axis of rotation. Therefore, as more mass is located further away from the rotation axis, the moment of inertia gets larger.

For the chosen answer, as an object's mass increases and is positioned farther away from the axis of rotation, each mass element contributes more significantly to the overall moment of inertia. This means that for the same amount of rotational force (torque), the object will experience a smaller angular acceleration than it would if more mass were concentrated closer to the axis.

In contrast, the other choices do not accurately capture the relationship between mass distribution and moment of inertia. Mass located near the axis does not decrease the moment of inertia; rather, it contributes less to it. The moment of inertia is not a constant value as mass is added or changed; it is directly influenced by how that mass is distributed relative to the rotation axis