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.

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

Solid Sphere: Lower rotational inertia (mass closer to the center). Hollow Sphere: Higher rotational inertia (mass further from the center).

Center of Mass: Minimum rotational inertia. Parallel Axis: Higher rotational inertia (due to the parallel axis theorem).

Hoop: Higher rotational inertia (mass concentrated at the rim). Solid Disk: Lower rotational inertia (mass distributed throughout).

Point mass: $I = mr^2$. Continuous object: $I = \int r^2 dm$

Doubling Mass: Rotational inertia doubles. Doubling Distance: Rotational inertia quadruples (due to the $r^2$ term).