Which concept refers to the resistance to a change in rotational speed, depending on distribution of mass and axis distance?

Which concept refers to the resistance to a change in rotational speed, depending on distribution of mass and axis distance?

• A. Angular velocity
• B. Torque
• C. Body type
• D. Moment of inertia

Answer: (D)

The key idea here is how hard it is to change how fast something spins depends on how its mass is spread around the rotation axis. This resistance is called the moment of inertia. It increases when more mass sits farther from the axis, because each bit of mass contributes to the total inertia by a amount proportional to the square of its distance from the axis (I = sum m r^2). So even with the same overall mass, shifting mass outward makes it harder to speed up or slow down the spin; more torque is needed to achieve the same change. Think of a figure skater: when the arms are extended, the distribution puts more mass farther from the axis, increasing moment of inertia and making changes in spin harder. When the arms are pulled in, I decreases, and the skater can rotate more easily for a given angular momentum. To distinguish the terms: angular velocity is simply the rate of rotation, not the resistance to change. Torque is what causes a change in rotation, but the question specifically describes the property that governs how much torque is needed—the moment of inertia.

The key idea here is how hard it is to change how fast something spins depends on how its mass is spread around the rotation axis. This resistance is called the moment of inertia. It increases when more mass sits farther from the axis, because each bit of mass contributes to the total inertia by a amount proportional to the square of its distance from the axis (I = sum m r^2). So even with the same overall mass, shifting mass outward makes it harder to speed up or slow down the spin; more torque is needed to achieve the same change.

Think of a figure skater: when the arms are extended, the distribution puts more mass farther from the axis, increasing moment of inertia and making changes in spin harder. When the arms are pulled in, I decreases, and the skater can rotate more easily for a given angular momentum.

To distinguish the terms: angular velocity is simply the rate of rotation, not the resistance to change. Torque is what causes a change in rotation, but the question specifically describes the property that governs how much torque is needed—the moment of inertia.