Relativistic Dynamics: Momentum, Energy, and Mass-Energy Equivalence

Manual: General · Subject: Physics

This lesson extends relativity to motion, force, and energy conservation.

When objects move near light speed

Relativistic momentum

Momentum becomes $p = \gamma mv,$ which grows faster than the classical expression $mv$ as $v$ approaches $c$ .

Total energy

The total energy of a particle is $E = \gamma mc^2,$ and the kinetic energy is $K = (\gamma - 1)mc^2.$

Mass-energy equivalence

A particle at rest still has energy $E_0 = mc^2.$ This rest energy shows that mass is a concentrated form of energy.

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Common misconception

Relativity does not say mass literally turns into energy in a simplistic way; rather, mass is one form of energy and total energy and momentum are conserved together.

What is the rest energy of a particle of mass $m$ ?

mc

m/c^2

mc^2

\gamma mc^2

Write the relativistic expression for momentum.

Energy problem-solving checklist

1

Step 1: Decide whether the particle is at rest or moving.
2

Step 2: Compute $\gamma$ from the speed.
3

Step 3: Use $E = \gamma mc^2$ and $K = (\gamma-1)mc^2$ if needed.
4

Step 4: Check that low-speed results reduce to $K \approx \tfrac12 mv^2$ .

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