Dimensions

measurement or amount of any given geometry that tells us many things about the measure’s content. The dimensions of an item are only the first thing we notice whenever we look at it. In actuality, our dimensions, such as height, elevation, and the number of muscular elements on our body, are also described or observed. The dimension of an object relates to how that might be assessed in terms of fundamental variables. Whenever we define a quantity’s measurement or dimension, we are effectively defining its identity and presence. Almost everything in the universe has a thickness, and weight, and occupies some space, and so does existence, as we can see.

Defining Dimensions

The dimensions of a specified amount or characteristic are the levels at which the basic fundamental elements are raised to convey a variable. Parentheses [ ] are used to reflect the dimensionality of the seven basic fundamental elements or characteristics.

Fundamental and Derived Dimensions

There are different dimensions of different quantities. But majorly there are two kinds of dimensions in physics, namely the fundamental and derived dimensions. The fundamentals are the basic ones from which are formulated such as mass, time, length or width and some others. 

Whereas, the derived quantities are formulated based on initially expanding the quantity and converting it to a fundamental form or using their units and formulating the dimension of the same. A few of them are, Power, Velocity, Work, Energy, etc.

Understanding the syntax of Dimensions and their usage

The dimension of height or length is represented by [L], that of endurance or time is marked by [T], mass is indicated by [M], the dimension of electrical charge or current is displayed as [A], and amount of substance is indicated by [mol]. Likewise, the dimension of temperature [k], and the new brightness intensity dimension of photons is [Cd]. Similarly, the dimensions of all physical quantities are represented using parentheses in which their symbol is inserted.

For more clarification,

Consider any quantitative measurements or variable M that is impacted by some of its basic variables, such as height or width, duration, mass, the amount of the material, electrical currents, and the heat surrounding it, when raised to powers or values m,n,o,p,q and r. As a result, the dimensions of such a specific physical measure M can be stated as follows:

[M] = [LmTnMomolpAqKr]

When expressing a parameter’s dimensions, we need to use the notation [ ]. All of everyday reality is defined in terms of duration or time, length, mass or volume.

Nevertheless, there is no need to memorise the dimensions of any physical quantity as they may be solved and determined until we have the formula and unit of it in mind (for complicated quantities they are defined in basic physical terms). We’ll look at some instances of variables to see how we might deduce them further.

Few examples of such dimensions

Let us now have a look at a few examples of dimensions of such quantities and how they are derived.

Dimensional formula of force,

The dimensional formula of force is derived using its formula, it is a type of derived quantity. The formula of force is F=Ma, where we got one fundamental quantity that is mass. For another further converting it to its unit as m/s2 for which the dimension will be [LT-2].

Therefore, that of force will be,

[F]=[MLT-2]

Where,

M is the dimension of mass and [LT-2] is the dimension of acceleration where L stands for length i.e., meter and T is for time i.e., second. 

Let us consider another example of Power,

If we write power in terms of work and time it will be written as,

P=[W][T]

And for them, as we’ve found the dimension of acceleration using its unit we’ll find the dimension of work and time using their dimensions which will come as, [L2MT-2] and [L0M0T1]

Therefore, the dimension of power will come as,

[P]=[L2MT-2]/[L0M0T1]

Subsequently,

[P]=[L2M1T-3]

Similarly, the dimensions of few more derived quantities are, [Ek]=[L2M1T-2] of kinetic energy,  [Ep]=[L2M1T-2] of potential energy, [V]=[L1M0T-1] of velocity, [D]=[L3M1T0] of density, etc.

Conclusion

Dimensional formulas of physical quantities or indeed any physical parameter assist us in analysing the properties of that measure or variable. Or, to put it another way, it tells us more about the structure of the very same. A complicated quantity’s dimensional formula can be obtained using its equation and afterwards corresponding SI units. Some of those are listed above, along with instances of equations. Power, for example, does have the dimensional formula of [P]=[L2M1T-3], kinetic energy does have the formula of [Ek]=[L2M1T-2], and so on.