Sum the individual rotational inertias: $\I_{\text{tot}} = \sum I_i = \sum m_i r_i^2$

1. Imagine the solid is made of tiny masses dm. 2. Use the integral: $I = \int r^2 dm$. 3. Integrate over the entire object.

1. Identify the axis of rotation. 2. Find the rotational inertia about the center of mass ($I_{cm}$). 3. Determine the distance d between the axes. 4. Calculate $I' = I_{cm} + Md^2$.

1. Define a mass element dm. 2. Express dm in terms of spatial variables. 3. Determine the limits of integration. 4. Evaluate the integral $I = \int r^2 dm$.

1. Identify each particle's mass ($m_i$) and distance ($r_i$) from the axis of rotation. 2. Calculate each particle's rotational inertia ($I_i = m_i r_i^2$). 3. Sum the individual rotational inertias: $I_{tot} = \sum I_i$.

Increases the rotational inertia.

Increases the rotational inertia.

The rotational inertia is minimized.

The object will experience a smaller angular acceleration.

The rotational inertia increases, as described by the parallel axis theorem.

A measure of an object's resistance to changes in its rotational motion.

Mass and how that mass is distributed relative to the axis of rotation.

The perpendicular distance of each mass element dm to the axis of rotation.

The rotational inertia about an axis through the center of mass.

The perpendicular distance between the new axis and the axis through the center of mass.