Which term is the rotational analog of mass?

Which term is the rotational analog of mass?

• A. Moment of Inertia
• B. Torque
• C. Angular Momentum
• D. Radius of Gyration

Answer: (A)

In rotational motion, inertia represents how hard it is to change the object's angular velocity. The quantity that captures this resistance is the moment of inertia, I, which depends on how the mass is distributed relative to the axis of rotation. It’s calculated as I = ∑ m_i r_i^2 or I = ∫ r^2 dm, so mass farther from the axis contributes more to the inertia. This ties directly to how rotation responds to torque: τ = I α, where torque is what tries to accelerate the rotation and α is the angular acceleration. So moment of inertia plays the same role in rotational dynamics that mass plays in linear dynamics. Other terms aren’t the same role. Torque is the cause that produces rotation, not the measure of resistance to changing that rotation. Angular momentum L = I ω is the rotational analogue of linear momentum p = m v, combining inertia with motion but not naming the inertia itself. The radius of gyration is a way to express I in terms of total mass via I = M k^2, but it’s still a derived quantity, not the direct measure of rotational inertia. So the term that serves as the rotational analog of mass is the moment of inertia.

In rotational motion, inertia represents how hard it is to change the object's angular velocity. The quantity that captures this resistance is the moment of inertia, I, which depends on how the mass is distributed relative to the axis of rotation. It’s calculated as I = ∑ m_i r_i^2 or I = ∫ r^2 dm, so mass farther from the axis contributes more to the inertia.

This ties directly to how rotation responds to torque: τ = I α, where torque is what tries to accelerate the rotation and α is the angular acceleration. So moment of inertia plays the same role in rotational dynamics that mass plays in linear dynamics.

Other terms aren’t the same role. Torque is the cause that produces rotation, not the measure of resistance to changing that rotation. Angular momentum L = I ω is the rotational analogue of linear momentum p = m v, combining inertia with motion but not naming the inertia itself. The radius of gyration is a way to express I in terms of total mass via I = M k^2, but it’s still a derived quantity, not the direct measure of rotational inertia.

So the term that serves as the rotational analog of mass is the moment of inertia.