🧭 Gyroscopic Precession Lab

Explore rigid body rotational mechanics ($\boldsymbol{\tau} = \boldsymbol{\Omega}_p \times \mathbf{L}$). Calculate steady precession velocity ($\Omega_p = \frac{mgr}{I_z \omega_s}$), nutation frequency, and sleeping top stability limits.

Spin Speed ($N_s$) RPM

Rotor Mass ($m$) kg

Flywheel Radius ($R$) Meters (6 cm)

Pivot Arm ($r_{cm}$) Meters from pivot

Cyan Arrow = Angular Momentum $\mathbf{L}$ | Yellow Circle = Precession Path

Precession Speed ($\Omega_p$)

2.08 rad/s

Period T = 3.02 s / rev

Angular Momentum ($L_s$)

0.452 J·s

$\omega_s = 314.2$ rad/s

Gravitational Torque ($\tau$)

0.941 N·m

$\mathbf{r}_{cm} \times m\mathbf{g}$

Nutation Frequency

100.0 Hz

Rapid wobble eigenmode

Gyroscopic Invariance Paradox: Spinning the rotor faster increases angular momentum $\mathbf{L}$, causing the precession rate $\Omega_p$ to slow down ($\Omega_p \propto 1/\omega_s$). Gravity is resisted without falling!