Question

The mass moment of inertia of an object is a measure of:

• A. Its resistance to changes in rotational motion about an axis
• B. The total mass distributed in the object
• C. Its ability to conduct heat
• D. The gravitational force acting on it

Hint:

Mass moment of inertia is the rotational equivalent of mass. It governs how much torque is needed to rotate a body at a given angular acceleration.

Answer 1

The Correct Option is A

Step 1: The mass moment of inertia (MMI) is a scalar quantity that represents how mass is distributed relative to an axis of rotation. It quantifies an object’s resistance to changes in its rotational motion.
Step 2: The moment of inertia is defined as: \[ I = \int r^2 \, dm \] where \( r \) is the perpendicular distance of the mass element \( dm \) from the axis of rotation.
Step 3: A larger mass moment of inertia implies the object is more resistant to angular acceleration under a given torque, as seen in the rotational form of Newton's second law: \[ \tau = I \alpha \] where \( \tau \) is torque, \( I \) is the moment of inertia, and \( \alpha \) is angular acceleration.
Why the other options are incorrect:

• (B) Total mass alone doesn't determine rotational behavior—distribution relative to the axis is key.
• (C) Heat conduction relates to thermal properties, not mechanical inertia.
• (D) Gravitational force depends on mass and gravity, not how the mass is distributed around an axis.