Dimensional Formula

In physics and mathematics, dimensional formulas are used to define quantities which are physical, as in quantities which can be observed through the plain eye. 

Since the advancement of mathematics and physics, maintaining and keeping track of equations gets harder, here dimensional formulas play a role in making equations easier. Furthermore, discussion on how to write dimensional formulas as well as  some important dimensional formulas like dimensional formula of force, dimensional force of velocity and dimensional formula of charge have been mentioned in the below sections.

What Are Dimensional Equations?

In physics and mathematics, dimensional formulas are used to define quantities which are physical, as in quantities which can be observed through the plain eye. 

Since the advancement of mathematics and physics, maintaining and keeping track of equations gets harder, here dimensional formulas play a role in making equations easier.

The five dimensions commonly used are:

Mass (M)

Length (L)

Time (T)

Electrical Current (I)

Temperature (K)

Most quantities that are physical have dimensional equations. These equations are nothing but formulas for units. One thing to remember is that dimensional formulas or quantities are not to be used as units of measures.

How To Write Dimensional Formulas?

Before discussing some important dimensional formulas like dimensional formula of force, dimensional force of velocity and dimensional formula of charge, it is mandatory to know how dimensional formulas are written in the scientific manner. This is discussed below:

These formulas are written in square brackets, [ ] and the dimensions, the five fundamental ones which are discussed above are written inside the square brackets.

The general formula is as follows;

[M𝒙 L𝒚 T𝒛]

The 𝒙, 𝒚, 𝒛 are the powers or exponents of that particular dimensional unit and when the exponents are negative, that means the exponent is in the denominator.

Let’s see what the dimensional formula for volume is. The general formula for volume being length x width x height that means there is no mass and there is no time dimension, and the length is three times and therefore the formula is [M0 L3 T0].

Dimensional Formula For Velocity

The general formula for velocity in physics is, distance/ time where distance can be considered as length and since there is no mass involved that component again attaians nil value. Since time is in the denominator.  -1 will be used.

Dimensional formula for velocity= [M0 L1 T-1]

Dimensional Formula For Force

Force is defined as mass into acceleration. For this dimensional formula, we need to know what the formula of acceleration is, which is velocity/ time so the dimensional formula of force has a mass component, two time components and one length component.

Dimensional formula for force= [M1 L1 T-2]

Dimensional Formula For Charge

The general formula is current x time. Since there is no mass involved, the mass component will be zero and length and time components will each have the power of one.

Dimensional formula for charge= [M0 L1 T1]

Conclusion

In physics and mathematics, dimensional formulas are used to define quantities which are physical, as in quantities which can be observed through the plain eye. 

Since the advancement of mathematics and physics, maintaining and keeping track of equations gets harder, here dimensional formulas play a role in making equations easier. 

Dimensional formula for velocity= [M0 L1 T-1]

Dimensional formula for force= [M1 L1 T-2]