Mass: A measure of an object's resistance to linear acceleration. Rotational Inertia: A measure of an object's resistance to angular acceleration; depends on mass and its distribution.

Hoop: Mass is distributed farther from the axis of rotation, resulting in higher rotational inertia. Solid Disk: Mass is distributed closer to the axis, resulting in lower rotational inertia.

Calculate the rotational inertia ($I = mr^2$) for each object and then sum them: $I_{tot} = \sum I = \sum mr^2$.

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

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: $I_{tot} = \sum I_i$.