Mass is one of the most fundamental quantities in physics and it's difficult to get through a physics course without getting a hang of basic formulas associated with it. Almost every fundamental physics equation has mass as a variable in it because it is an inseparable quantity.
What is Mass?
Mass is an inherent property of matter in all its forms. It should not be confused with weight. Weight is the force of gravity acting on a mass, whereas mass is a measure of matter content that responds to gravity and has the property of inertia. There are two defined types of it. One is inertial mass and the other is gravitational mass. The former is the property of matter that offers resistance to change by a force. The latter is the property of matter, which exerts the gravitational force. The inertial and gravitational masses were shown to be equal, by the Eötvös experiment. In the SI system of units, mass has the unit of 'Kilogram (Kg)'.
There are various physics equations, that can yield the value of mass. Each one of them is useful in deriving its value, given certain known quantities.
Calculating it Using Density and Volume
When the density and volume of any substance are known, it is possible to calculate its mass.
Mass (in Kilograms) = Density (in Kg per m3) x Volume (in m3)
Formula For Center of Mass
Center of mass is the point in a body, where the whole mass can be hypothetically assumed to be concentrated. It is a function of the individual masses of particles and their relative positions with respect to each other. It can only be defined for rigid bodies, who have fixed positions of particles.
R (Center of Mass) = (m1r1 + m2r2 + m3r3. . + miri) / (m1 + m2 + m3. . + mi)
= (Σ miri) / (Σ mi)
Thus, the center of mass is calculated as a ratio of individual masses, weighed by position vectors and total mass of the whole body of particles.
Formula For Molecular Mass
The atomic mass formula derives the masses of atoms, in comparison to 1/12th the mass of a carbon C12 atom. All these masses are derived experimentally. A molecule is a collection of atoms bonded together. So, the molecular mass is the sum of individual masses of atoms bonded in it.
Molecular Mass = Σ (Mass of an Atom x Number of Atoms)
Molar Mass Formula
Molar mass of a molecule or substance is simply the molecular weight expressed in grams. Its unit is gm/mole.
Molar Mass = (Molecular Weight) x 1 g/mol
Formula For Mass in Newtonian Mechanics
Mass (in Kg) = Force (in Newtons)/Acceleration (Meter/s2)
So, knowing the acceleration of a body and the force acting on it, you can easily calculate its mass.
Special Relativistic Formula
Special relativity changed the way we see the world. It demolished the notion of absolute time which was prevalent in Newtonian mechanics and it is now known to be relative. In mechanics, based on the special relativity, everything is dependent on the frame of reference, except the speed of light in vacuum, which remains constant. Here is the relativistic formula:
m = (m0)/(√(1 - v2/c2))
where m0 is rest mass of the particle, v is the velocity of the particle, and c is the velocity of light.
Recently, physicists have provided a hypothesis which tries to explain how particles of matter acquire mass. The theory says that there is a Higgs field pervading all space, which interacts with all matter. A particle acquires mass, through its interaction with the Higgs boson. Current experiments at CERN's 'Large Hadron Collider (LHC)' are aimed at finding the Higgs boson. One day, we will know how matter acquires mass.