## Inertial Mass, Gravitational Mass and Weight

We mislead ourselves when we say we are measuring the mass of an object. If fact we are measuring the force of gravity on that object and changing that force into a mass using a calibrated scale. If we were to 'measure' the mass of an object at different points on the Earth's surface using the same scale operating on a spring for example, we would get a different result, though the mass of a body is supposedly a constant. This is because mass and weight are related via the equationThoughmay be a constant, g varies over the Earth's surface, hence the the weight will vary over the Earth's surface. For a pair of weighing scales calibrated tothe measured mass will vary slightly different according to where on the Earth's surface the measurement is take.

In addition mass is not a single concept. It has two aspects – gravitational mass and inertial mass.

The inertial massis that property of an object that determines how it responds to a given force.  Different masses subject to the same force F experience different accelerations, with the acceleration being given by the equationThe units of inertial mass are

Gravitational mass is that mass which appears in Newton's Law of universal gravitation:It determines the forces acting on two objects of gravitational masses andseparated by a distance r. Different gravitational masses experience different gravitational forces.

To within the limits of experimental observation,so there is in fact only one measurement of mass. This implies for example that two bodies of different masses experience the same acceleration (ignoring for example, air resistance) when brought close to a massive body like the Earth, since the forceand on two bodies of massandboth at distancefrom a body of massare given by

and

Thenand

Obviously then