Explore the vector nature of angular momentum $\vec{L} = I\vec{\omega}$ and its conservation in isolated systems. Visualize how torque changes angular momentum over time, and analyze collisions involving rotating objects where total angular momentum remains constant.
Apply calculus to motion analysis using $v = \frac{dx}{dt}$ and $a = \frac{dv}{dt}$, and integrate acceleration to find velocity and position functions. Visualize how derivatives and integrals connect position, velocity, and acceleration graphs in real-time.
Calculate moment of inertia $I = \int r^2 dm$ for various geometric shapes and apply the parallel axis theorem $I = I_{cm} + Md^2$. Visualize how mass distribution affects rotational inertia and compare common shapes like disks, spheres, and rods.
Analyze rolling motion with the no-slip condition $v_{cm} = R\omega$ and explore energy partitioning between translational and rotational kinetic energy. Visualize objects rolling down inclines and see how moment of inertia affects acceleration.
Calculate the center of mass for multi-particle systems using $\vec{r}_{cm} = \frac{\sum m_i\vec{r}_i}{\sum m_i}$ and analyze 2D collision dynamics. Visualize how momentum conservation applies independently to x and y components in elastic and inelastic collisions.