Types of Kinetic Energy:

Soumendra Nath Thakur

ORCiD: 0000-0003-1871-7803

28-09-2024

There are at least two types of kinetic energy:

Mechanical Kinetic Energy:

In extended classical mechanics, mechanical kinetic energy adheres to the classical mass-energy equivalence principle. However, it also involves negative apparent mass or the negative effective mass of dark energy.

This form of energy is associated with atomic changes, such as shifts in electron energy, photon re-emission, or the release of free electrons (e.g., thermionic emission). Mechanical kinetic energy plays a crucial role in motion and gravitational dynamics, integrating both classical and relativistic effects, including classical deformation of matter and relativistic Lorentz transformations. It is observable in gravitationally bound systems and in regions influenced by dark energy.

Key Equations:

Gravitating Mass:

Mɢ = Mᴍ + (−Mᵃᵖᵖ)

Mɢ = Mᴍ + Mᴅᴇ 

Kinetic Energy:

KE ∝ −Mᵃᵖᵖ

KE ∝ Mᴅᴇ

Total Energy (Classical):

Eᴛₒₜ = PE + KE

Eᴛₒₜ = (Mᴍ + (−Mᵃᵖᵖ)) + KE

Follows Motion Equation:

Effective Force:

F = (Mᴍ + (−Mᵃᵖᵖ))⋅aᵉᶠᶠ

Follows Gravitational Equation:

Fɢ = G·(Mᵉᶠᶠ·M₂)/r²,

• M₂ = (Mᴍ₂ + (−M₂ᵃᵖᵖ))

• Mᵉᶠᶠ = Mᴍ + (−Mᵃᵖᵖ) = Mɢ

Relativistic Kinetic Energy:

This form of kinetic energy adheres to the relativistic mass-energy equivalence principle and is associated with positive mass. It involves atomic energy changes within the nucleus and is only realizable within gravitationally bound systems.

Key Equations:

Total Energy (Relativistic):

E² = (ρc)² + (mc²)²

Rest Energy:

E = m·c² when: v=0, hence, ρ=0