Equivalence of Inertial and Gravitational Mass in Classical Mechanics.

15-09-2024

The equivalence principle in classical mechanics posits that inertial mass (Mᴍ) is equal to gravitational mass (Mɢ), i.e., 

Mᴍ = Mɢ.

Given that:

Inertial mass is related to acceleration by:

Mᴍ = F/a

Gravitational mass is expressed as:

Mɢ = Fɢ·r²/G·Mᴍ

Thus, the equivalence principle (Mᴍ = Mɢ) leads to:

F/a = Fɢ·r²/G·Mᴍ

This equation shows that the force (F) causing acceleration (a) due to an object’s inertial mass is equivalent to the gravitational force (Fɢ) exerted by mass (Mᴍ) at a distance (r), scaled by the gravitational constant (G).

Interpretation:

The equivalence principle demonstrates that an object's resistance to acceleration (inertial mass) is indistinguishable from its gravitational interaction (gravitational mass), highlighting the fundamental relationship between gravity and inertia in classical mechanics.

This principle is key to understanding both classical and relativistic physics, illustrating the balance between gravitational and inertial forces through r, a, and G.

#EquivalencePrinciple #ClassicalMechanics