obsidianvault/physics/Torque and Rotational Dynamics/Rotational Inertia.md

Torque and Rotational Dynamics For a point mass:$I=mr^2$ I is rotational inertia (kg * m^2) m is mass r is radial distance

Several discrete objects:

I_{tot}=\Sigma I_i=\Sigma m_i r^2

Parallel Axis Theorem

Essentially shifting the axis and calculating the new inertia.

I'=I_{cm}+Md^2

• $I$' is rotational inertia about the parallel axis (kg⋅m²)
• $I_{cm}$ is rotational inertia about the center-of-mass axis (kg⋅m²)
• $M$ is the total mass of the system (kg)
• $d$ is the perpendicular distance between the two parallel axes (m)