Rotational Dynamics & Gyroscopic Precession Virtual Laboratory

Vector Cross-Product Mechanics: Verify Euler's rotational equation ($\vec{\tau} = \frac{d\vec{L}}{dt}$) by observing how a downward gravitational force produces a horizontal torque perpendicular to $\vec{L}$, causing the gyroscope to precess horizontally rather than topple. Inverse Spin Speed Law: Demonstrate that increasing rotor spin velocity ($\omega_s$) increases angular momentum ($L = I\omega_s$), which inversely reduces the precession rate ($\Omega_p = \tau / L$). Moment of Inertia ($I$) Comparison: Evaluate how mass distribution alters rotational inertia across four geometries: Solid Disk ($I = \frac{1}{2}Mr^2$), Thin Hoop/Rim ($I = Mr^2$), Thick Annular Ring ($I = 0.625Mr^2$), and Solid Sphere ($I = \frac{2}{5}Mr^2$). Right-Hand Rule & Spin Inversion: Invert rotor spin direction ($+L \leftrightarrow -L$) to observe the immediate reversal of azimuthal precession direction. Nutation & Equilibrium: Examine trochoidal nutation oscillations ($\omega_n$) when released from non-equilibrium tilt, and verify zero precession ($\Omega_p = 0$) when the pivot coincides with the center of mass ($d = 0$).