MEC-50

Gyroscopic torque

Steady rotor precession.

Reading speed

MachinesGyroscopic torque

Governing equation

\tau=I\omega\Omega

$\Omega \in \left[0.1, 20\right]$

where

I: I (kg·m²)
\omega: Spin (rad/s)
\Omega: Precession (rad/s)
\tau: Torque (N·m)

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

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①

Governing law — red

\tau=I\omega\Omega

$\Omega \in \left[0.1, 20\right]$

$\Omega = 0.1$ $\tau = 2$

Along the curve

②

Domain of the variable — blue

\Omega_{\min} = 0.1,\quad \Omega_{\max} = 20

$\Omega \in \left[0.1, 20\right]$

$\Omega = 0.1$ $\Omega = 0.1$

Along the curve

③

Response curve — green

\tau=I\omega\Omega

$\Omega \in \left[0.1, 20\right]$

$\Omega = 0.1$ $\tau = 2$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}\tau}{\mathrm{d}\Omega}

$\Omega \in \left[0.1, 20\right]$

$\Omega = 0.225$ $\tau^{\prime} = 20$

Along the curve

Lecture brief

Historical brief

Machine design grew from Coulomb torsion and Hertz contact (1881) through Soderberg fatigue and the heat-engine cycle. The lab writes shaft, bearing, contact and thermodynamic limits in SI. This sheet (MEC-50 — Gyroscopic torque) is the form associated with Gyroscopic torque. Working symbols: $I$ , $\omega$ , $\Omega$ $\rightarrow$ $\tau$ . Steady rotor precession. Pedagogical SI sheet with a live model and a swept parameter.

Purpose

Purpose: compute

\tau

from

I

\omega

\Omega

in Mechanical via

\tau=I\omega\Omega

Steady rotor precession. Use it when a real mechanical question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

I = 0.050\,\mathrm{kg·m^{2}}

\omega = 400.000\,\mathrm{rad/s}

\Omega = 2.000\,\mathrm{rad/s}

, the governing relation

\tau=I\omega\Omega

yields

\tau = 40.000\,\mathrm{N·m}

. One governing identity, SI units, a single sweep on the sheet. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

I I0.05 kg·m²Spin \omega400 rad/sPrecession \Omega2 rad/s

Outputs

Torque \tau40.000 N·m

Reading speed

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Narration of this film

One governing identity, SI units, a single sweep on the sheet.

Steady rotor precession. Pedagogical SI sheet with a live model and a swept parameter.

Reading speed

Watch on YouTube