CLS-02

Translational kinetic energy

K = ½ m v².

Reading speed

EnergyVis viva / Kelvin

Governing equation

K=\tfrac12 m v^2

where

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

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

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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