## 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 equation Though may 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 to the 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 mass is 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 equation The 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 and separated 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 force and on two bodies of mass and both at distance from a body of mass are given by and Then and Obviously then 