Gravitational Inertia

Gravitational mass

Gravitational mass is measured with the use of a double-pan or triple-beam balance. It is a static measurement - that is, a measurement that can only be accurately recorded when the system is in a state of rest. This method involves placing an unknown mass on the pan and using countermasses to return the balance to equilibrium.

This type of measurement only works in the presence of gravity and is actually based on the torque produced by the product of the weights and their lever-arms' distance from the axis of rotation. Since torques produce rotation, when the clockwise torque caused by the countermasses equals the counterclockwise torque caused by the unknown mass, we say that the balance is in equilibrium. Since the balance will then be in a state of rest, we can read the correct value for the unknown's gravitational mass from the balance's scale.

Inertial Mass

Inertial mass is measured with the use of an inertial balance, or spring-loaded pan. It is a dynamic measurement - that is, a measurement that can only be accurately recorded while the system is in a state of motion. This method capitalizes on an object's inertia, or its tendency to continue in its current state of motion, as a means of quantifying the amount of matter present.

The pan is first calibrated by counting the number of vibrations in a specified amount of time produced by two objects whose masses are known. From this information, the period (represented with the variable T) of each object's mass is calculated by dividing the total amount of time by the total number of vibrations. Period is usually measured in terms of seconds per vibration. These two periods are then plotted on a graph of T2 vs Mass.

Subsequent knowledge of the vibrational period of any unknown mass will allow its inertial mass to be interpolated from this calibration graph. This type of balance will measure an object's inertial mass even in the absence of gravity.

Spring Balance

A spring balance consists of a coiled spring which is fixed to a support and hook at the other end to which the body to be weighed is applied. Within the spring's limit of elasticity, the distance through which it is stretched is directly proportional to the weight of the applied body. A pointer and graduated scale attached to the spring convert this distance into a weight reading.