The kilogram is one of the SI base units. It is often confused with weight, however, mass is a measurement of matter while weight is a measurement of the force of gravity on an object.
Your body’s weight changes depending on your position on Earth but its mass stays the same. This is because gravity is a net force.
Active Gravitational Mass
Gravimeters are the standard instrument for making gravity surveys on land, at sea, in boreholes and in aircraft. They work by comparing the length of a mass-loaded spring to a reference instrument that is fixed on Earth’s surface. Changing the weight of the fixed mass changes the gravity and produces a change in spring length that is recorded by optical, mechanical or electrical means.
Since the 17th century, many experiments have tested whether inertial and passive gravitational mass differ from one another. These tests have confirmed the equivalence of inertial and passive gravitational mass, which is what Newton’s third law requires. But it does not tell us why these two different types of mass must always be identical, a point that Einstein’s general theory of relativity addressed by developing the concept of active gravitational mass. This is the force that determines an object’s acceleration when it is acted upon by other objects. This force is proportional to the product of an object’s inertial and passive gravitational masses divided by its equivalence constant, which has been measured with high precision.
Passive Gravitational Mass
Passive gravitational mass is the reaction of an object to gravity, its weight. It can be measured in a number of ways, including using the Cavendish experiment and weighing scales that take g into account.
Gravitational mass is important because it is a factor in an object’s inertia, the resistance to the force of gravity. However, despite its significance, the distinction between inertial and passive gravitational mass is rarely made in physics experiments. In countries that use the imperial system, it’s even more confusing as the unit pound is used for both mass and force!
In this paper, I argue that the equivalence of inertial and passive gravitational mass must be considered a hidden assumption in the literature. This leads me to question the conclusions of Mana et al 2022[72] regarding the definition of kilogram and how it can be experimentally realized through the atom count method. In the process, some deeper issues concerning the literature of matter wave interferometers are unraveled.
Inertial Mass
Inertial mass is the measure of resistance to changes in motion and, by extension, the strength of an object’s gravitational attraction. It determines how easy or difficult it is for a force to accelerate or decelerate an object.
In physics, an object’s inertial mass is proportional to its net force of acceleration and inversely proportional to its mass. This is the basis of Newton’s second law, F = ma, which equates inertial and gravitational mass.
Until the time of Newton, “mass” was synonymous with an object’s downward force, also known as its weight. This was a useful concept because it allowed an individual’s physical well-being to be measured with a simple balance. However, since the development of atomic and particle physics, it has become clear that different atoms and elementary particles, with the same amount of matter, can have different masses. This has led to a definition of the term “mass” that is more conceptually distinct but physically equivalent, namely, inertial mass.
Kinetic Energy
In physics, kinetic energy is the force that causes a body to move from a state of rest to a state of movement at a specified speed. This type of energy increases proportionally to the mass and velocity of the body, according to Newton’s Law of Inertia. The body’s kinetic energy will remain constant unless another force acts on it to increase or decrease its velocity and, hence, its kinetic energy.
When an object is moving, it possesses not only translational kinetic energy but also rotational kinetic energy. The total kinetic energy of the object is the sum of its translational kinetic energy and the rotational kinetic energy around its center of mass.
Kinetic energy is a scalar quantity, meaning that it is solely described by magnitude, and not direction, while velocity has both a magnitude and a direction. This is one of the many ways in which kinetic energy differs from its more familiar cousin, potential energy.