Gravitational and inertial mass

We can of the mass of an object in two different ways, and it is therefore important to see how they are connected.
Consider:
(a) the mass that governs how fast an object will accelerate when a given force acts on it, known as the inertial mass (m_i);
(b) the mass that governs the gravitational attractive force between two bodies, known as the gravitational mass (m).

The two equations giving these quantities are:
F = m_ia and F = GmM/R²

But GM/R² = g_o
Therefore: F = mg_o = W (the weight of the mass).

We can derive the simple pendulum equation using: W = mg_o    - mg_ox/L = m_ia
So the period (T) is given by:


Experiments show that m_i/m = 1 to a high degree of accuracy and so m_i = m. Thus inertial mass and gravitational mass are equivalent.