MEC-45

Shaft power

Instantaneous mechanical power.

Reading speed

MachinesShaft power

Governing equation

P=T\omega

$\omega \in \left[1, 400\right]$

where

T: Torque (N·m)
\omega: Rate (rad/s)
P: Power (kW)

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

P=T\omega

$\omega \in \left[1, 400\right]$

$\omega = 1$ $P = 0.08$

Along the curve

②

Domain of the variable — blue

\omega_{\min} = 1,\quad \omega_{\max} = 400

$\omega \in \left[1, 400\right]$

$\omega = 1$ $\omega = 1$

Along the curve

③

Response curve — green

P=T\omega

$\omega \in \left[1, 400\right]$

$\omega = 1$ $P = 0.08$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}P}{\mathrm{d}\omega}

$\omega \in \left[1, 400\right]$

$\omega = 3.509$ $P^{\prime} = 0.08$

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-45 — Shaft power) is the form associated with Shaft power. Working symbols: $T$ , $\omega$ $\rightarrow$ $P$ . Instantaneous mechanical power. Pedagogical SI sheet with a live model and a swept parameter.

Purpose

Purpose: compute

P

from

T

\omega

in Mechanical via

P=T\omega

Instantaneous mechanical power. Use it when a real mechanical question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

T = 80.000\,\mathrm{N·m}

\omega = 150.000\,\mathrm{rad/s}

, the governing relation

P=T\omega

yields

P = 12.000\,\mathrm{kW}

. 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

Torque T80 N·mRate \omega150 rad/s

Outputs

Power P12.000 kW

Reading speed

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Narration of this film

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

Instantaneous mechanical power. Pedagogical SI sheet with a live model and a swept parameter.

Reading speed

Watch on YouTube