CLS-02

Translational kinetic energy

K = ½ m v².

Reading speed

EnergyVis viva / Kelvin

Governing equation

K=\tfrac12 m v^2

$v \in \left[0, 200\right]$

where

m: Mass (kg)
v: Speed (m/s)
K: Kinetic energy (J)

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.

00:0 / 00:08

①

Governing law — red

K=\tfrac12 m v^2

$v \in \left[0, 200\right]$

$v = 0$ $K = 0$

Along the curve

②

Domain of the variable — blue

v_{\min} = 0,\quad v_{\max} = 200

$v \in \left[0, 200\right]$

$v = 0$ $v = 0$

Along the curve

③

Response curve — green

K=\tfrac12 m v^2

$v \in \left[0, 200\right]$

$v = 0$ $K = 0$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}K}{\mathrm{d}v}

$v \in \left[0, 200\right]$

$v = 1.258$ $K^{\prime} = 2.516$

Along the curve

Lecture brief

Historical brief

Newtonian mechanics (1687) plus energy, angular momentum, Kepler and the ballistic parabola remain the first language of motion. Every sheet here is a closed-form orbit, throw, spin or oscillator. This sheet (CLS-02 — Translational kinetic energy) is the form associated with Vis viva / Kelvin. Working symbols: $m$ , $v$ $\rightarrow$ $K$ . The work–energy theorem integrates F·dx = m v dv to ½ m v², the kinetic energy of a particle.

Purpose

Purpose: compute

K

from

m

v

in Classical mechanics via

K=\tfrac12 m v^2

K = ½ m v². Use it when a real classical mechanics question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

m = 2.000\,\mathrm{kg}

v = 10.000\,\mathrm{m/s}

, the governing relation

K=\tfrac12 m v^2

yields

K = 100.000\,\mathrm{J}

. Particle, inertial frame, no rotation. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Mass m2 kgSpeed v10 m/s

Outputs

Kinetic energy K100.000 J

Reading speed

Watch on YouTube

Free library

Full library

Free PDF / open book

YouTube channels

00:0 / 00:08

Narration of this film

Particle, inertial frame, no rotation.

The work–energy theorem integrates F·dx = m v dv to ½ m v², the kinetic energy of a particle.

Reading speed

Watch on YouTube