Inertial mass and Gravitational mass

Before we learn the differences, we first define the concept of force. Newton gave us two definition of force,
$$F=ma$$and $$F=G\frac{m_{1}m_{2}}{r^{2}}$$where, the symbols represents the usual meaning.

In short, the "$m$" term in the first definition of force is referred to as inertial mass and the "$m_{1},m_{2}$" in the definition for the force in second one is defined as the gravitational mass.

Gravitational mass is measured by comparing the force of gravity of an unknown mass to the force of gravity of a known mass. This is typically done with some sort of balance scale.

Inertial mass is found by applying a known force to an unknown mass, measuring the acceleration, and applying Newton's Second Law, $m = F/a$. This gives as accurate a value for mass as the accuracy of your measurements. When the astronauts need to be weighed in outer space, they actually find their inertial mass in a special chair which contains springs.

The interesting thing is that, physically, no difference has been found between gravitational and inertial mass. Many experiments have been performed to check the values and the experiments always agree to within the margin of error for the experiment. Einstein used the fact that gravitational and inertial mass were equal to begin his Theory of General Relativity in which he postulated that gravitational mass was the same as inertial mass and that the acceleration of gravity is a result of a 'valley' or slope in the space-time continuum that masses 'fell down' much as pennies spiral around a hole in the common donation toy at your favorite chain store.

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